In 2001, Dorcas Weiner (Weiner) was involved in two separate car accidents and sustained back and neck injuries. She filed benefit claims with her insurer, Commerce Insurance Company (Commerce), pursuant to the underinsured motorist *564(UIM) provision of her policy. After the parties were unable to settle the claims, they entered into arbitration as required by the insurance contract. On March 9, 2006, a Superior Court judge granted the motion of Weiner and her husband, Raymond (Raymond2), to vacate the resulting arbitration award and ordered that a new arbitrator be appointed. The second arbitrator submitted an award substantially more favorable to the Weiners. This award subsequently was confirmed by a second Superior Court judge, and Commerce now appeals, arguing that the first judge erred in vacating the original award because (1) the first arbitrator did not exceed his authority and the original award was not contrary to law or public policy, (2) if at all, the matter should have been submitted for reconsideration by the first arbitrator, not a second one, and (3) if at all, only a portion of the original award should have been vacated. We affirm.

1. Background. On January 26, 2001, Weiner was the passenger in a vehicle that was struck from behind by another vehicle. Weiner sustained injury to her back and neck, and settled with the driver of the other vehicle for $20,000. Weiner had incurred $1,580.35 in medical and chiropractic bills when, on March 6, 2001, she was involved in a second car accident, in Pennsylvania. Weiner was the passenger in her daughter-in-law’s vehicle when it was struck by another vehicle, driven by Scott Harlan. Weiner claimed that this second accident exacerbated her existing injury, to the point where she experienced continual neck and back pain.

After the second accident, Weiner filed suit against Harlan in Pennsylvania; Harlan cross-claimed against Weiner’s daughter-in-law (the other driver). Before that litigation was complete, Weiner filed a claim under the UIM provision of her Commerce policy. The UIM provision covered Weiner for up to $100,000, and she filed claims relating to both accidents. Weiner and Commerce could not agree on the amount, if any, due her under the UIM provision, and thus, as the policy required, the parties entered into arbitration. The UIM provision states that “[t]he determination as to whether an injured person is legally entitled to recover damages from the legally responsible owner or operator will be by agreement between us and the injured person. The *565amount of damages, if any, will be determined in the same way. Arbitration will be used if no agreement can be reached.” The parties agreed to arbitrate the claims regarding both car accidents at the same time.

The first arbitrator entered his award on August 4, 2005. As to the first accident, the arbitrator found that the $20,000 Weiner already had received was “sufficient” to cover those injuries. As to the second accident, the arbitrator found that Weiner’s existing injuries were exacerbated, but declared that the claim as to that accident was premature, because “there potentially is sufficient bodily injury insurance covered by Mr. Harlan and the claimant’s daughter-in-law to cover her award.” The arbitrator did not foreclose Weiner from renewing her claim under her UIM provision, should Harlan’s insurance be insufficient to cover any award or settlement received in Pennsylvania.

The Weiners brought a motion to vacate the award, successfully arguing that, by deciding that a portion of the claim was premature and not determining damages, the first arbitrator had exceeded his authority or entered a judgment contrary to law or public policy. The first judge agreed and appointed a second arbitrator (chosen from a “list maintained by the clerk’s office”), who reviewed the case and entered an award in July of 2006. As to the first accident, the second arbitrator awarded Weiner $40,000 for her injuries and Raymond $7,500 for his loss of consortium. As to the second accident, the second arbitrator rejected any prematurity argument and awarded Weiner $40,000 for her injuries and Raymond $7,500 for his loss of consortium.

2. Motion to vacate the August 4, 2005, arbitration award. The first arbitrator plainly erred when he concluded that the Weiners’ claims under the UIM provision were premature, as it is well settled that an insurance company “has a present obligation to arbitrate the . . . defendant’s demand for underinsurance benefits, notwithstanding the pendency of a claim against an individual allegedly liable for the injuries.” Aetna Cas. & Sur. Co. v. Faris, 27 Mass. App. Ct. 194, 194 (1989). Nonetheless, arbitration awards are subject to very limited judicial review, and even “a grossly erroneous [arbitration] decision” typically is binding. Lynn v. Thompson, 435 Mass. 54, 61-62 (2001), quoting from Trustees of Boston & Me. Corp. v. Massachusetts Bay Transp. Authy., 363 Mass. 386, 390 (1973). See Boston *566Housing Authy. v. National Conference of Firemen & Oilers, Local 3, 458 Mass. 155, 161 (2010) (“Generally speaking, an arbitrator enjoys considerable latitude in fashioning an arbitration award”). We thus confine our review to whether the first arbitrator exceeded his powers under the contract, or made an award that is against law or public policy; in either event, the award must be vacated.3 G. L. c. 251, § 12(a)(3). Boston Housing Authy., supra (“The question whether an arbitrator acted in excess of his authority is always open for judicial review”).

“An arbitrator exceeds his authority by granting relief beyond the scope of the arbitration agreement...[,] by awarding relief beyond that to which the parties bound themselves ...[,] or by awarding relief prohibited by law.” Superadio Ltd. Partnership v. Winstar Radio Prod., LLC, 446 Mass. 330, 334 (2006), quoting from Plymouth-Carver Regional Sch. Dist. v. J. Farmer & Co., 407 Mass. 1006, 1007 (1990). “Arbitration, it is clear, may not ‘award relief of a nature which offends public policy or which directs or requires a result contrary to express statutory provision’ ... or otherwise transcends the limits of the contract of which the agreement to arbitrate is but a part.” Ibid., quoting from Lawrence v. Falzarano, 380 Mass. 18, 28 (1980).

The first arbitrator exceeded his authority by failing to determine the Weiners’ damages and instead deferring that determination and making it contingent on the results of the Pennsylvania litigation. Specifically, he declared, “ [A]t this time I award [Weiner] nothing for her injuries for March 6, 2001 until such time as the issues in Pennsylvania are adjudicated.”4 Under the terms of the UIM provision, arbitration is the sole forum available to the parties for dispute resolution, and an arbitrator is contractually required to decide whether the insured is entitled to damages and in what amount. However, the first arbitrator’s award makes clear his intention to accept as valid whatever damages award a Pennsylvania fact finder might reach, rather *567than making that determination himself, as required by the UIM provision.5 This failure to act within the bounds of the contract amounted to a violation of G. L. c. 251, § 12(a)(3). See Superadio Ltd. Partnership, supra at 337 (“The [arbitrator]’s authority derives from the parties’ agreement”); Grobet File Co. of America, Inc. v. RTC Sys., Inc., 26 Mass. App. Ct. 132, 134-135 (1988) (“the arbitrator may not ignore the plain words of the contract”), citing United Paperworkers Intl. Union v. Misco, Inc., 484 U.S. 29, 40-41 (1987). Compare Greene v. Mari & Sons Flooring Co., 362 Mass. 560, 563 (1972), quoting from United Steelworkers of America v. Enterprise Wheel & Car Corp., 363 U.S. 593, 599 (1960) (“The parties bargained for [the arbitrator’s] final interpretation of their collective bargaining agreement. They got what they bargained for”); Sheriff of Suffolk County v. AFSCME Counsel 93, Local 419, 68 Mass. App. Ct. 222, 226 (2007). The case of Danvers v. Wexler, 12 Mass. App. Ct. 160 (1981), does not compel a different result.6’7

3. Appointment of a second arbitrator. Even if Commerce had not waived the point, as it did, we discern no error in the first judge’s appointment of a second arbitrator. The relevant statute states that “if the award is vacated on grounds set forth in clauses (3) and (4) of paragraph (a)[8] the court may order a rehearing before the arbitrators who made the award or their *568successors appointed in accordance with section three.” G. L. c. 251, § 12(c), inserted by St. 1960, c. 374, § 1. Section 3 of G. L. c. 251 states that if an arbitrator “fails or is unable to act and his successor has not been duly appointed, the court on application of a party shall appoint an arbitrator.” G. L. c. 251, § 3, inserted by St. 1960, c. 374, § 1. Although Commerce argued that the original award should not be vacated, it did not oppose the Weiners’ request that a second arbitrator be appointed. The first judge, having implicitly determined that the first arbitrator had failed to act under the contract, appropriately exercised his authority under the statute to appoint a second.

4. Vacating the award in its entirety. Commerce contends that the first judge erred in vacating the original award in its entirety because the first arbitrator properly addressed liability and damages as to the first accident, another issue that Commerce did not raise below. Indeed, Commerce admitted in its answer that the “agreement of the parties provided . . . [tjhat both motor vehicle accidents be consolidated and submitted to one (1) and the same arbitrator at one (1) arbitration hearing to be decided by that one (1) arbitrator at the same time.” The issue is waived. Hoffman v. Houghton Chem. Corp., 434 Mass. 624, 639 (2001) (“The consequence of the failure properly to object at trial is to waive the issue on appeal”).9

Judgment affirmed.