Hudson appeals the district court’s grant of Secretary Bowen’s motion for summary judgment. The district court found that substantial evidence supported the Secretary’s conclusion that Hudson had $4,000 in excess resources and thus could not continue receiving supplemental security income benefits. On appeal, Hudson argues that (1) the Secretary’s determination of excess resources was not supported by substantial evidence; (2) the standards used to determine resources are unfair because they create an irrebuttable presumption of ineligibility; and (3) the case should be remanded so the Secretary can consider new evidence on Hudson’s expenditure of the $4,000 in excess revenue.

FACTS

On March 5, 1985, Hudson appeared before an Administrative Law Judge (AU) to appeal the termination of his supplemental security income benefits. He was represented by counsel and given an opportunity to prove that his income was below the threshold level despite the receipt of a $20,-000 personal injury award. With regard to the $4,000 at issue in this appeal, Hudson testified that he spent the money gambling in Reno. No objective evidence or other testimony was introduced to verify his report. The AU did not find Hudson’s testimony credible and, because Hudson presented no other explanation concerning the $4,000, the AU determined that Hudson had not shown why he was eligible to continue receiving benefits.

The Appeals Council reviewed the AU’s decision and considered some new evidence on a theory not presented to the AU, that the $4,000 was depleted through living expenses. The Appeals Council affirmed the AU’s decision, finding that Hudson had failed to prove that he no longer had the excess resources. The district court agreed, granting Bowen’s motion for summary judgment. We affirm.

DISCUSSION

The district court’s grant of Bowen’s motion for summary judgment is reviewed de novo and is appropriate if no genuine issue of material fact exists. Miller v. Heckler, 770 F.2d 845, 847 (9th Cir.1985). The Secretary’s factual finding that Hudson had $4,000 in excess income is conclusive if supported by substantial evidence. Id. See 42 U.S.C. § 405 (g). Substantial evidence is “more than a mere scintilla” and is such that a reasonable mind may accept it as adequate to support a conclusion. Miller, 770 F.2d at 848 .

In its review, the district court correctly noted that resolving, the issue of whether Hudson had spent or retained $4,000 of the personal injury award hinged on an assessment of his credibility. Credibility assessments are often necessary in hearings before an AU. An AU, for example, may have to determine whether the claimant is in pain, and there may be no evidence presented on this issue beyond the claimant’s own testimony. See e.g., Taylor v. Heckler, 765 F.2d 872 (9th Cir.1985). In Taylor , this court held that an AU is free to disregard a claimant’s self-serving statements if they are unsupported by objective findings. Id. at 876 . Similarly, in determining whether a claimant has spent or retained excess resources, an AU must be free to disregard self-serving statements that cannot be verified, and the AU’s assessment of credibility must be given great weight. See Nyman v. Heckler, 779 F.2d 528, 531 (9th Cir.1985).

If an AU’s decision is based on a credibility assessment, there must be an explicit finding as to whether the claim ant’s testimony was believed or disbelieved and the testimony must not be entirely discounted simply because there was a lack of objective findings. Cotton v. Bowen, 799 F.2d 1403, 1407 (9th Cir.1986); Lewin v. Schweiker, 654 F.2d 631, 635 (9th Cir.1981). Here, the AU stated that he found Hudson’s testimony that he spent the $4,000 gambling in Reno to be “not credible.” The AU’s opinion reveals that he relied to a large extent, although not entirely, on the lack of any objective evidence. He also noted that he doubted Hudson’s credibility because Hudson had made inconsistent statements regarding the number of trips he made to Reno. Thus, the record supports the AU’s credibility determination. In addition, the district court noted two further reasons that the AU had to doubt Hudson’s credibility: Hudson had failed to report the receipt of the $20,000 personal injury award, and he had failed to report income received in 1981 and 1982. We accept those findings and hold that Hudson failed to show that he was eligible to continue receiving benefits.

Hudson asserts that objective evidence will often be unavailable in cases of this nature. He argues that current standards used to determine resources create a conclusive presumption of ineligibility to claimants with no objective proof of expenditures. He suggests that the Secretary consider prorating excess income over a period of time at least to limit a claimant’s period of ineligibility. Even if no formal prorating scheme is adopted, however, Hudson argues that the Secretary should logically presume that the money was depleted through ordinary living expenses during the six month time period between the termination of Hudson’s benefits and his hearing before the AU.

Hudson never advanced this depletion theory to the AU, however, and he presented no evidence or testimony in support of it. There is no presumption that money not accounted for is expended and given Hudson’s history of receiving support from his family, the AU could not have been expected simply to presume, without any evidence of expenditure, that the $4,000 was depleted through living expenses rather than saved. While Hudson did present the depletion theory, and some new evidence on it, to the Appeals Council, the Council determined that the affidavit submitted did not establish that Hudson no longer had excess resources.

Hudson now contends that he was never given the opportunity to fully present evidence that the money was depleted through living expenses. He argues, therefore, that the case should be remanded to allow the Secretary to consider such evidence. The record does not support Hudson’s assertion that he was denied an opportunity to present his evidence. Hudson would simply like a second opportunity, but our function is to review the correctness of the Secretary’s decision at the time it was made. Remand to consider additional evidence is not appropriate; as noted by the Appeals Council and the district court, the place to advance a new theory or introduce new evidence after a hearing before an AU is in a new benefits application to the Administration. We hold, therefore, that remand is not proper, and that the Secretary’s decision was based on substantial evidence.

CONCLUSION

For the reasons stated above, we affirm the district court’s grant of Bowen’s motion for summary judgment.

. While the suggested prorating schemes are worthy, our review is limited, under 42 U.S.C. § 405 (g), to evaluating factual findings under the substantial evidence standard and checking conformity with and validity of the Secretary’s regulations. § 405(a) grants "full power” to the Secretary to establish procedures that provide for the "nature and extent of the proofs and evidence ... to establish the right to benefits." . Hudson did eventually pursue this route and is currently receiving benefits.