*823The defendants1 appeal from the judgments of the trial court confirming an arbitration award in favor of the plaintiffs.2 On appeal, the defendants claim that the court erred in denying their motion to vacate the award and in granting the plaintiffs' motion to confirm the award because the arbitrator failed to disclose a conflict of interest, failed to order production of certain *1174evidence and exceeded her powers under the arbitration agreements. We disagree. Accordingly, we affirm the judgments of the trial court.
The following facts, as set forth by the trial court in its April 11, 2016 memorandum of decision, and procedural history are relevant to this appeal. "These consolidated cases3 arise out of the plaintiffs' investment in three limited partnerships: Giddings Oil & Gas, L.P. (Giddings, L.P.), Hunton Oil Partners, L.P. (Hunton, L.P.), and ASYM Energy Fund III, L.P. (ASYM, L.P.). The plaintiffs are investors and limited partners in each of these limited partnerships. Each of the limited partnerships had a general partner which is a limited liability company: Giddings Genpar, LLC (Giddings Genpar), Hunton Oil Genpar, LLC (Hunton Genpar), and ASYM [Capital] III, LLC (ASYM Genpar), respectively.
*824"Each of the limited liability companies that served as a general partner of a limited partnership had a manager; the manager of Giddings Genpar was Giddings Investments, LLC, the manager of Hunton Genpar was Glenrose Holdings, LLC, and the manager of ASYM Genpar was ASYM Energy Investments, LLC. The plaintiffs in their complaint alleged that the individual defendant Gregory Imbruce ... exercised complete control over the managers and therefore over the general partners and over the limited partnerships. The various companies which acted as general partners and/or managers, as well as Imbruce individually, will be collectively referred to as the ... defendants. The plaintiffs brought this action individually and derivatively on behalf of the three limited partnerships.
"In their second amended complaint4 (in docket number CV-12-6014987-S) the plaintiffs alleged various fact patterns pursuant to which they asserted that the ... defendants have made misrepresentations in the marketing of the investments, that the ... defendants have violated the provisions of the Connecticut Uniform Securities Act (CUSA), [ General Statutes § 36b-2 et seq. ], and that the ... defendants have wrongfully diverted assets of the various limited partnerships to their own purposes or accounts. The second amended complaint sounds in [eleven] counts which seek both injunctive relief and monetary damages, alleging counts that sound in fraud, breach of fiduciary duty, conversion, civil theft, and violation of the Connecticut Unfair Trade Practices Act (CUTPA), General Statutes § 42-110b et seq., among other theories of relief. The prayer for relief in the second amended complaint seeks both equitable relief and monetary damages.
*825"The case of Starboard Resources, Inc. v. Henry , Superior Court, judicial district of Stamford, Docket No. CV-12-6015112-S (Starboard case), is an interpleader action in which Starboard Resources, Inc. (Starboard), seeks, inter alia, an order of the court authorizing it to deposit the disputed shares in court and a judicial determination regarding the relative rights of the parties to those shares.
*1175"On July 11, 2014, the court granted the motion of the ... defendants to stay these actions pending completion of arbitration proceedings, some of which had already begun.... Consistent with the court order staying this action, the parties proceeded to arbitration and by subsequent agreement broadened the arbitration beyond that which they had previously agreed to in their limited partnership agreements.5 The parties proceeded with the arbitration before a single arbitrator.
"On September 10, 2015, the arbitrator rendered an award in favor of the plaintiffs herein, who as respondents in the arbitration proceeding had filed a counterclaim, including allegations similar in nature to the allegations of the second amended complaint previously described. The award consisted of declaratory awards, monetary damages, awards of [attorney's] fees, *826interest, injunctive relief requiring an accounting, post-judgment interest, as well as awards of arbitration fees and costs." (Footnotes added and omitted.)
On September 14, 2015, the plaintiffs filed a motion in the trial court to confirm the arbitration award. On October 13, 2015, the defendants filed an objection to the plaintiffs' motion to confirm the award and a cross motion to vacate the award accompanied by scores of exhibits. A flurry of procedural and substantive filings followed, until, on February 8, 2016, the court held a hearing on the parties' respective motions. The court, after further briefing, rendered judgments in accordance with the arbitrator's decision on April 11, 2016, confirming the arbitral award. This appeal followed. Additional facts and procedural history will be set forth as necessary.
We begin with applicable legal principles. The court found, and the parties agree, that these cases, though brought in state court, are governed by the federal Arbitration Act, 9 U.S.C. §§ 1 through 16 (arbitration act), because the underlying contracts involve interstate commerce.6 "Arbitration is essentially a creature of contract, a contract in which the parties themselves charter a private tribunal for the resolution of their disputes.... Arbitration agreements are contracts *1176and their meaning is to be determined ... under accepted rules of [state] contract law .... *827"Judicial construction of an arbitration agreement, however, is not guided solely by the principles of relevant state contract law. The arbitration act; 9 U.S.C. §§ 1 through 16 ; governs written arbitration agreements that pertain to contracts involving interstate commerce.... The arbitration act creates a body of federal substantive law of arbitrability, applicable to any arbitration agreement within the coverage of the [a]ct .... As federal substantive law ... the arbitration act is to be applied by state courts as well as by federal courts....
"The purpose of the arbitration act is to ensure that private agreements to arbitrate are enforced according to their terms.... The arbitration act establishes a strong federal policy favoring arbitration.... [W]hen Congress passed the [a]rbitration [a]ct in 1925 ... [i]t intended courts to enforce [arbitration] agreements into which parties had entered ... and to place such agreements upon the same footing as other contracts ...." (Citations omitted; footnote omitted; internal quotation marks omitted.) Hottle v. BDO Seidman, LLP , 268 Conn. 694, 701-703, 846 A.2d 862 (2004).
Accordingly, the court's review of an arbitration award is "extremely limited." Burns International Security Services, Inc. v. International Union, United Plant Guard Workers of America (UPGWA) and its Local 537 , 47 F.3d 14, 17 (2d Cir. 1995). Courts may vacate an arbitrator's decision "only in very unusual circumstances." First Options of Chicago, Inc. v. Kaplan , 514 U.S. 938, 942, 115 S.Ct. 1920, 131 L.Ed.2d 985 (1995). "Following issuance of an arbitration award, § 9 of the [arbitration act] provides that a party may apply to a [trial] court 'for an order confirming the award, and thereupon the court must grant such an order unless the award is vacated, modified, or corrected as prescribed in sections 10 and 11 of this title.' "
*828STMicroelectronics, N.V. v. Credit Suisse Securities (USA), LLC , 648 F.3d 68, 74 (2d Cir. 2011). "Only a barely colorable justification for the outcome reached by the arbitrators is necessary to confirm the award." (Internal quotation marks omitted.) D.H. Blair & Co. v. Gottdiener , 462 F.3d 95, 110 (2d Cir. 2006). Accordingly, "[a] party petitioning a ... court to vacate an arbitral award bears the heavy burden of showing that the award falls within a very narrow set of circumstances delineated by statute and case law." Duferco International Steel Trading v. T. Klaveness Shipping A/S , 333 F.3d 383, 388 (2d Cir. 2003). Specifically, under the arbitration act, an arbitration award may be vacated only "(1) where the award was procured by corruption, fraud, or undue means; (2) where there was evident partiality or corruption in the arbitrators, or either of them; (3) where the arbitrators were guilty of misconduct in refusing to postpone the hearing, upon sufficient cause shown, or in refusing to hear evidence pertinent and material to the controversy; or of any other misbehavior by which the rights of any party have been prejudiced; or (4) where the arbitrators exceeded their powers, or so imperfectly executed them that a mutual, final, and definite award upon the subject matter submitted was not made." 9 U.S.C. § 10 (a) (2012).7
*1177Given these limitations on a court's review of the arbitration award, "[w]e review a [trial] court's decision to confirm or vacate an arbitration award de novo on questions of law and for clear error on findings of fact."
*829National Football League Management Council v. National Football League Players Assn. , 820 F.3d 527, 536 (2d Cir. 2016) ; see also Kellogg v. Middlesex Mutual Assurance Co. , 326 Conn. 638, 645, 165 A.3d 1228 (2017) (reviewing trial court's vacatur de novo). We turn now to the defendants' claims.
I
The defendants first claim that the court should have vacated the arbitration award because the arbitrator failed to disclose a conflict of interest. Specifically, the defendants argue that the arbitrator was required to disclose the fact that she had arbitrated the personal divorce of an attorney, Kenneth Votre, who represented Imbruce and Glenrose Holdings, LLC, in a separate but related malpractice action. We do not agree.
An arbitration award may be vacated "where there was evident partiality or corruption in the arbitrators ...." 9 U.S.C. § 10 (a) (2) (2012). "Evident partiality may be found only where a reasonable person would have to conclude that an arbitrator was partial to one party to the arbitration.... Although a party seeking vacatur must prove evident partiality by showing something more than the mere appearance of bias ... [p]roof of actual bias is not required.... Rather, partiality can be inferred from objective facts inconsistent with impartiality.... A showing of evident partiality must be direct and not speculative." (Citations omitted; internal quotation marks omitted.) Kolel Beth Yechiel Mechil of Tartikov, Inc. v. YLL Irrevocable Trust , 729 F.3d 99, 104 (2d Cir. 2013). The party seeking vacatur must prove evident partiality by "clear and convincing evidence." Id., at 106. "[T]he evident-partiality standard [is] not satisfied because the undisclosed relationship at issue was too insubstantial to warrant vacating the award.... [W]here an undisclosed matter is not suggestive of bias, vacatur based upon that nondisclosure *830cannot be warranted under an evident-partiality theory." (Citations omitted; internal quotation marks omitted.) Scandinavian Reinsurance Co. Ltd. v. Saint Paul Fire & Marine Ins. Co. , 668 F.3d 60, 72-73 (2d Cir. 2012). Indeed, "there is no duty to disclose if the relationship is trivial." Uhl v. Komatsu Forklift Co., Ltd. , 512 F.3d 294, 307 (6th Cir. 2008). Nevertheless, "arbitrators must take steps to ensure that the parties are not misled into believing that no nontrivial conflict exists. It therefore follows that where an arbitrator has reason to believe that a nontrivial conflict of interest might exist, he must (1) investigate the conflict ... or (2) disclose his reasons for believing there might be a conflict and his intention not to investigate.... [A] failure to either investigate or disclose an intention not to investigate is indicative of evident partiality." (Citations omitted.) Applied Industrial Materials Corp. v. Ovalar Makine Ticaret Ve Sanayi, A.S. , 492 F.3d 132, 138 (2d Cir. 2007).
The defendants argue that the purported conflict was nontrivial and that the arbitrator misled them into believing that no nontrivial conflict existed. Specifically, the defendants contend that they were misled because the arbitrator's initial disclosures *1178at the start of the arbitration suggested that she considered any prior arbitral relationships to be per se nontrivial, but the arbitrator then failed to disclose her arbitral relationship with Attorney Votre. We are not persuaded. The conflict here alleged, if one existed, was merely trivial-regardless of the substance of the arbitrator's initial disclosures.
In its memorandum of decision, the court found that "[t]he divorce arbitration did not involve any of the parties to the subject arbitration. The divorce arbitration did not involve any of the attorneys or witnesses to the subject arbitration. The divorce arbitration involved an attorney who did not participate in the subject arbitration and did not represent any of the *831defendants or any other parties in the subject arbitration. The divorce arbitration involved an attorney who represented some of the defendants in a completely unrelated matter."
The defendants argue, however, that the arbitrator's adverse decision in Attorney Votre's divorce, and the Superior Court's subsequent vacatur8 thereof, evince such bias against Attorney Votre that a reasonable person would have to conclude that the arbitrator was predisposed to rule against any party tangentially affiliated with him. We are not persuaded. The United States Court of Appeals for the Second Circuit has "repeatedly said that adverse rulings alone rarely evidence partiality, whether those adverse rulings are made by arbitrators ... or by judges ...." (Citations omitted.) Scandinavian Reinsurance Co. Ltd. v. Saint Paul Fire & Marine Ins. Co. , supra, 668 F.3d at 75 ; see also Burton v. Mottolese , 267 Conn. 1, 49, 835 A.2d 998 (2003) ( "adverse rulings do not amount to evidence of bias"), cert. denied, 541 U.S. 1073, 124 S.Ct. 2422, 158 L.Ed.2d 983 (2004). The Superior Court's vacatur of the arbitrator's award in Attorney Votre's divorce does not give substance to the defendants' speculative claim, especially where the vacatur was premised on a statutory *832ground other than evident partiality. See footnote 8 of this opinion.
There being no indicia of bias, the arbitrator's involvement in her professional capacity in a "completely unrelated matter" is too attenuated to be of any consequence in the underlying arbitration. The Second Circuit has held that "to disqualify any arbitrator who had professional dealings with one of the parties (to say nothing of a social acquaintanceship) would make it impossible, in some circumstances, to find a qualified arbitrator at all." Morelite Construction Corp. v. New York City District Council Carpenters Benefit Funds , 748 F.2d 79, 83 (2d Cir. 1984). The arbitrator's prior arbitration involving Attorney Votre did not give rise to a material relationship with a party that would require disqualification.
*1179Scandinavian Reinsurance Co. Ltd. v. Saint Paul Fire & Marine Ins. Co. , supra, 668 F.3d at 74 ("overlapping arbitral service [is] not a material relationship with a party ... such as a family connection or ongoing business arrangement with a party or its law firm-circumstances in which a reasonable person could reasonably infer a connection between the undisclosed outside relationship and the possibility of bias for or against a particular arbitrating party" [citation omitted; internal quotation marks omitted] ).
Nevertheless, the defendants argue that the arbitrator's initial disclosures defined what kind of relationship is nontrivial for the purposes of this arbitration. That is, the defendants argue that the arbitrator's disclosure of some previous arbitrations involving one of the parties' law firms necessitates the disclosure of all previous arbitrations involving one of the parties' law firms. In support of this contention, the defendants rely principally on Applied Industrial Materials Corp. v. Ovalar Makine Ticaret Ve Sanayi, A.S. , supra, 492 F.3d 132, and New Regency Productions, Inc. v. Nippon Herald Films, Inc. , 501 F.3d 1101 (9th Cir. 2007). Their reliance *833is misplaced. In the former, the United States Court of Appeals for the Second Circuit vacated an arbitration award because the arbitrator, the chief executive officer of a third party corporation, having first disclosed that he had become aware of contract negotiations between his subsidiary and a party's parent company, failed to investigate and disclose that, in fact, a contract already existed. Applied Industrial Materials Corp. v. Ovalar Makine Ticaret Ve Sanayi, A.S. , supra, at 138. In the latter, the United States Court of Appeals for the Ninth Circuit vacated an arbitration award where the arbitrator, having disclosed past negotiations on behalf of a previous employer with people who later became executives of one of the parties, failed to disclose his new employer's past negotiations with a film producer who was affiliated with one of the parties. New Regency Productions, Inc. v. Nippon Herald Films, Inc. , supra, at 1110 ("it is precisely against the background of previously disclosed information that [the arbitrator's] failure to disclose his new position might have 'misled' [the defendant] 'into believing that no nontrivial conflict exist[ed],' " citing Applied Industrial Materials Corp. v. Ovalar Makine Ticaret Ve Sanayi, A.S. , supra, at 137 ).
Neither case is analogous to the present one; the conflicts in those cases are material, substantial business relationships in which the arbitrator had a specific, material interest. The purported conflict here is arbitral service in two completely unrelated matters. Logically, for an arbitrator to "mislead" a party into believing that no nontrivial conflict exists, a nontrivial conflict must in fact exist. As we have stated, any purported conflict here is trivial, as a reasonable person would not have to conclude that it made the arbitrator partial to one party to the arbitration. See Kolel Beth Yechiel Mechil of Tartikov, Inc. v. YLL Irrevocable Trust , supra, 729 F.3d at 106. Accordingly, the trial court did not err in *834declining to vacate the arbitration award for evident partiality.
II
The defendants next claim that the court erred in confirming the arbitration award where the arbitrator failed to order production of relevant and probative evidence from the plaintiffs and allowed the plaintiffs to amend their counterclaim to allege new claims for which discovery was not allowed. The defendants argue that each of these errors individually, or, in the alternative, that all of these errors together, *1180amounted to misconduct in violation of 9 U.S.C. § 10 (a) (3). We do not agree.
"Courts have interpreted [§] 10 (a) (3) to mean that except where fundamental fairness is violated, arbitration determinations will not be opened up to evidentiary review. In making evidentiary determinations, an arbitrator need not follow all the niceties observed by the federal courts.... However, although not required to hear all the evidence proffered by a party, an arbitrator must give each of the parties to the dispute an adequate opportunity to present its evidence and argument.... Federal courts do not superintend arbitration proceedings. Our review is restricted to determining whether the procedure was fundamentally unfair. See Teamsters, Chauffeurs, Warehousemen, Helpers & Food Processors, Local Union 657 v. Stanley Structures, Inc. , 735 F.2d 903, 906 (5th Cir. 1984) ; accord Concourse Beauty School, Inc. v. Polakov , 685 F.Supp. 1311, 1318 (S.D.N.Y. 1988) ( [t]he misconduct must amount to a denial of fundamental fairness of the arbitration proceeding in order to warrant vacating the [award, quoting] Transit Casualty Co. v. Trenwick Reinsurance Co. Ltd. , 659 F.Supp. 1346, 1354 [S.D.N.Y. 1987], aff'd mem., 841 F.2d 1117 [2d Cir. 1988] )." (Citations omitted; internal quotation marks omitted.)
*835Tempo Shain Corp. v. Bertek, Inc. , 120 F.3d 16, 20 (2d Cir. 1997). "Under the [arbitration act's] extremely limited standard of review for vacatur requests, [trial] courts are not empowered to second-guess such decisions-procedural or substantive-even if there is evidence that the arbitrator erred." ARMA, S.R.O. v. BAE Systems Overseas, Inc. , 961 F.Supp.2d 245, 264 (D.D.C. 2013).
The Connecticut Supreme Court has held that arbitral misconduct violates a party's right to a fundamentally fair arbitration hearing if that misconduct is substantially prejudicial. "[T]o vacate an arbitrator's award on the ground of misconduct under [General Statutes] § 52-418 (a) (3),9 the moving party must establish that it was substantially prejudiced by the improper ruling.... This requirement that the moving party establish substantial prejudice is consistent with the showing that this court requires to order a new trial when a trial court makes an improper evidentiary ruling in a civil trial....
"Federal case law considering whether an arbitrator's evidentiary ruling deprived a party of a fair hearing is consistent with requiring the moving party to demonstrate substantial prejudice to vacate an award on this ground. One federal court analogized to the standard of review accorded trial courts' evidentiary rulings and declined to vacate an arbitrator's award because 'it cannot be said as a matter of law that [the excluded evidence] was decisive or that its exclusion was seriously harmful in the light of the other evidence in the case.' " (Citations omitted; footnote added.) Bridgeport v. Kasper Group, Inc. , 278 Conn. 466, 476-77, 899 A.2d 523 (2006), quoting *836Newark Stereotypers' Union No. 18 v. Newark Morning Ledger Co. , 397 F.2d 594, 599 (3d Cir.), cert. denied, 393 U.S. 954, 89 S.Ct. 378, 21 L.Ed.2d 365 (1968).
The defendants argue that the arbitrator should have (1) ordered production of documents relating to the valuation of Starboard, (2) ordered production of the statements made by the plaintiffs' attorney to the Department of Banking, (3) ordered production of communications between and *1181among the plaintiffs and their attorney and (4) denied the plaintiffs' motion to amend their counterclaim or at least allowed further discovery thereon. Because the defendants cannot demonstrate substantial prejudice, and, therefore, a denial of fundamental fairness, we are not persuaded.
A
First, the defendants argue that the arbitrator should have compelled the plaintiffs to turn over documents pertinent to the valuation of Starboard because its value was central to the defendants' claim of damages. The arbitrator, however, found that the plaintiffs were not liable to the defendants. As a result, any evidence-or lack thereof-as to the defendants' damages would not have affected the award. The defendants, therefore, cannot establish substantial prejudice. See Odeon Capital Group, LLC v. Ackerman , 864 F.3d 191, 194 (2d Cir. 2017) (holding that petitioner must demonstrate material nexus between allegation of fraud under 9 U.S.C. § 10 [a] [1], and award); Karppinen v. Karl Kiefer Machine Co. , 187 F.2d 32, 34-35 (2d Cir. 1951) (affirming arbitration award where perjured material evidence was nonetheless "extremely remote"); Rintin Corp., S.A. v. Domar, Ltd. , 374 F.Supp.2d 1165, 1170 (S.D. Fla. 2005) ("[p]laintiff has not shown how the discovery it claims it was unable to obtain is relevant, or would have affected the Award in any material respect"), aff'd, 476 F.3d 1254 (11th Cir. 2007). Thus, even if we assume, arguendo, that the arbitrator erred in refusing to compel *837discovery of the valuation material, such error did not affect the award. The arbitrator's refusal to compel discovery of it, therefore, is not substantially prejudicial and, thus, is not fundamentally unfair.
B
Second, the defendants have admitted that they have "no idea" what the communications with the Department of Banking, which may have been relevant to the defendants' defenses against the plaintiffs' CUSA claim, contain. The defendants speculate that the documents may reveal "impeachment material, damaging admissions by the [p]laintiffs, contradictions or other facts which were and remain unknown to the [defendants]." The arbitrator concluded that these documents were privileged. The defendants nevertheless argue that because they were deprived of the opportunity to examine these documents, they were denied a full and fair hearing. This argument is unavailing.
"The [arbitration act] does not bestow on a party the right to receive information about every matter that it might consider important or useful in presenting its case." Scandinavian Reinsurance Co. Ltd. v. Saint Paul Fire & Marine Ins. Co. , supra, 668 F.3d at 77. The defendants' speculative assertions about what the requested documents may have contained do not demonstrate prejudice, and, thus, fundamental unfairness. The defendants had ample opportunity to challenge the plaintiffs' CUSA counterclaim in the arbitration. Throughout the preliminary stages of arbitration and in the hearing itself, the defendants offered several defenses, produced testimony as to those defenses, introduced numerous exhibits in support thereof, and thoroughly cross-examined the plaintiffs' witnesses. Thus, the court correctly concluded that the defendants were not deprived of a fair hearing. See Tempo Shain Corp. v. Bertek, Inc. , supra, 120 F.3d at 20. Therefore, *838even if we assume, without deciding, that the arbitrator erred in concluding that the documents were privileged, the defendants are unable to demonstrate substantial prejudice *1182resulting in a violation of their right to a full and fair hearing.
C
Third, the defendants argue that they were prejudiced by the arbitrator's decision not to compel production of communications between and among the plaintiffs, their attorney, Jonathan Whitcomb, and erstwhile plaintiff, William Pettinati, who later aligned with Imbruce. The defendants contend that there was no privilege protecting these communications, and that even if there was, Pettinati waived the privilege by filing a grievance against Attorney Whitcomb. Additionally, the defendants argue that the arbitrator clearly was biased because she ordered discovery of their own communications with their former law firm, Levett Rockwood, P.C. The plaintiffs counter that the documents remained privileged because they were created in the then common interest of the plaintiffs, Pettinati and Attorney Whitcomb, an interest that the plaintiffs still hold in common with their attorney. The plaintiffs also argue that the defendants filed a malpractice claim against Levett Rockwood, and thereby waived any privilege.
Once more, the arbitrator's conclusions are entitled to great deference. See ARMA, S.R.O. v. BAE Systems Overseas, Inc. , supra, 961 F.Supp.2d at 264. Even if we assume, without deciding, that the arbitrator erred in her application of the legal principles underlying the various privileges and waivers asserted, the defendants cannot demonstrate substantial prejudice, and, thus, fundamental unfairness: They again admit that the contents of the communications at issue are unknown to them, arguing only that they are "potentially relevant and dispositive" without demonstrating how or why.
*839Indeed, the defendants are merely disputing the merits of the arbitrator's conclusion rather than whether the conclusion resulted from the violation of their right to a fundamentally fair hearing. This is not the evidence of misconduct the arbitration act requires.
D
Fourth, the defendants argue that they were prejudiced by the arbitrator's decision to allow the plaintiffs to amend their counterclaim after the conclusion of discovery and less than three weeks before the hearing. Specifically, the defendants contend that the plaintiffs waived and/or withdrew several claims they then realleged, namely, a CUTPA claim, a civil theft claim and alter ego claims against Imbruce personally. We are not persuaded.
The arbitrator has broad discretion to allow amendments to pleadings. See Saphir v. Neustadt , 177 Conn. 191, 206, 413 A.2d 843 (1979) ("a trial court may allow, in its discretion, an amendment to pleadings before, during, or ... after trial to conform to the proof"); see also Certain Underwriters at Lloyd's London v. Ashland, Inc. , 967 A.2d 166, 175 (D.C. 2009) ("we note that pleading requirements in arbitration proceedings are generally relaxed"). That discretion notwithstanding, the defendants still cannot demonstrate that the arbitrator's decision substantially prejudiced them such that the arbitration was fundamentally unfair. The amended counterclaims at issue were based on the same factual allegations present in the plaintiffs' original complaint. The defendants had long been on notice of these allegations. See Briere v. Greater Hartford Orthopedic Group, P.C. , 325 Conn. 198, 206-10, 157 A.3d 70 (2017) (reasserting relation back doctrine, by which pleadings may be amended if same operative facts control). Moreover, the arbitrator allowed mutual *840amendments to the parties' *1183claims, expressly conditioned on closure of discovery. Accordingly, the defendants cannot demonstrate substantial prejudice resulting in fundamental unfairness.
For those reasons, the arbitration proceedings culminated in a hearing that was not fundamentally unfair, during which both sides had an adequate opportunity to present their evidence and arguments. We therefore conclude that the court did not err in granting the plaintiffs' motion to confirm the arbitration award and denying the defendants' motion to vacate it for arbitral misconduct under 9 U.S.C. § 10 (a) (3).
III
Finally, the defendants claim that the court should have vacated the arbitration award pursuant to 9 U.S.C. § 10 (a) (4) because the arbitrator exceeded her authority. Specifically, the defendants argue that the arbitrator lacked the authority (1) to render an award against Imbruce individually, and (2) to apportion costs and impose attorney's fees. We disagree.
A
The defendants first contend that the arbitrator lacked the authority to enter an award against Imbruce individually. This argument is close to frivolous. In its memorandum of decision, the trial court found the following: "[I]n [their] original motion to stay this litigation in favor of arbitration the defendants, including Imbruce, asserted and represented to the court 'defendants are ready and willing to proceed with the arbitration of the plaintiffs' claims.' ... In the demand for arbitration Imbruce is named as a claimant and in his amended demand he also includes himself as a claimant. At the time he made the [m]otion to [s]tay and asserted that he was willing to proceed with the arbitration of [the] plaintiffs' claims, he knew the plaintiffs *841were asserting claims against him individually based upon the filed complaint. At no time did he expressly or impliedly suggest that the arbitration should exclude claims against him individually. In fact, the filings express the opposite position.
"While he voluntarily submitted his claims to arbitration and by his representations expressed that he was willing to arbitrate the plaintiffs' claims, he did not assert in any way lack of jurisdiction of the arbitrator to hear the plaintiffs' counterclaims against him personally, as he would have been required to do under the rules of the American Arbitration Association and, particularly, Rule 7c."
We turn now to applicable legal standards. "[A] party cannot be required to submit to arbitration any dispute which he has not agreed so to submit. Yet, to be consistent with congressional policy in favor of settlement of disputes by the parties through the machinery of arbitration, the judicial inquiry ... must be strictly confined to the question [of] whether the reluctant party did agree to arbitrate ... or did agree to give the arbitrator power to make the award he made." United Steelworkers of America v. Warrior & Gulf Navigation Co. , 363 U.S. 574, 582, 80 S.Ct. 1347, 4 L.Ed.2d 1409 (1960). There are "five theories for binding nonsignatories to arbitration agreements: 1) incorporation by reference; 2) assumption; 3) agency; 4) veil-piercing/alter ego; and 5) estoppel." Thomson-CSF, S.A. v. American Arbitration Assn. , 64 F.3d 773, 776 (2d Cir. 1995).
Although the plaintiffs claim that all five theories are implicated here, they focus their argument on the assumption and alter ego theories. Because we agree that Imbruce assumed the obligation to arbitrate, we do not consider the other *1184theories. "In the absence of a signature, a party may be bound by an arbitration clause if its subsequent conduct indicates that it is *842assuming the obligation to arbitrate." Id., at 777, citing Gvozdenovic v. United Air Lines, Inc. , 933 F.2d 1100, 1105 (2d Cir.), cert. denied, 502 U.S. 910, 112 S.Ct. 305, 116 L.Ed.2d 248 (1991). Here, as the facts previously indicated, Imbruce's conduct belies his claim that he is not bound by the arbitration. The demand for arbitration included Imbruce as a named party, and he repeatedly represented himself both at the trial court and in the arbitration as involved in and bound by the arbitration. Despite being on notice that the plaintiffs were asserting claims against him, Imbruce did not argue that he was not a party until after the arbitrator rendered her award. Imbruce therefore assumed the obligation to arbitrate and is responsible for the award rendered against him.
B
The defendants next contend that the arbitrator exceeded her authority under the arbitration agreements by apportioning costs and imposing attorney's fees. Specifically, the defendants argue that the parties agreed only to arbitrate the partnership agreements, which were silent as to costs and fees, and that the plaintiffs made no claim for costs and fees under the release agreement. This also borders on the frivolous.
The trial court found that both parties "asserted claims for fees and costs that they incurred." "If both parties sought attorney's fees ... then both parties agreed pro tanto to submit that issue to arbitration, and the arbitrators had jurisdiction to consider that issue and to award them." U.S. Offshore, Inc. v. Seabulk Offshore, Ltd. , 753 F.Supp. 86, 92 (S.D.N.Y. 1990) ; see also Commercial Arbitration Rules of the American Arbitration Association Rule R-47 (d) ("[t]he award of the arbitrator(s) may include ... an award of attorneys'
*843fees if all parties have requested such an award or it is authorized by law or their arbitration agreement").10
Moreover, once bound to arbitration, "[a] party seeking relief under [ § 10 (a) (4) ] bears a heavy burden. It is not enough ... to show that the [arbitrator] committed an error-or even a serious error.... Because the parties bargained for the arbitrator's construction of their agreement, an arbitral decision even arguably construing or applying the contract must stand, regardless of a court's view of its (de)merits .... Only if the arbitrator act[s] outside the scope of his contractually delegated authority ... may a court overturn his determination.... So the sole question for [the appellate court] is whether the arbitrator (even arguably) interpreted the parties' contract, not whether he got its meaning right or wrong." (Citations omitted; internal quotation marks omitted.) Oxford Health Plans, LLC v. Sutter , U.S., 569 U.S. 564, 133 S.Ct. 2064, 2068, 186 L.Ed.2d 113 (2013). Under this standard, we do not disturb an arbitrator's interpretation of her authority over an unrestricted submission. Here, the submission contained no express restrictions as to these issues, and we note that the parties agreed to expand the scope of the arbitration beyond the original agreements. See footnote 5 of this opinion. Accordingly, the arbitrator's interpretation of the scope of the arbitration agreements, including *1185whether she was empowered to award attorney's fees and costs, must stand.
In conclusion, therefore, the court did not err in granting the plaintiffs' application to confirm the arbitration award and denying the defendants' application to vacate it. The defendants cannot demonstrate that the arbitrator's conduct amounted either to evident partiality, misconduct or an excess of authority. See *8449 U.S.C. § 10 (a) (2012). Where none of these claimed statutory grounds for vacatur exists, the arbitration act requires a reviewing court to confirm the arbitration award. The court properly did so.
The judgments are affirmed.
In this opinion the other judges concurred.