SUMMARY ORDER

Plaintiffs-appellants appeal from (1) the judgment of the United States District Court for the District of Connecticut (Ar-terton, J.), dismissing their claims against all defendants, and (2) the denial of their motion to modify the judgment to grant leave to file an amended complaint. We assume the parties’ familiarity with the underlying facts and procedural history of this case, as well as the issues presented on appeal.

We conclude that the district court correctly held that the Consolidated Amended Complaint (the “Complaint”) failed to state a claim for securities fraud. Long before the price of Star Gas Partners, L.P. (“Star Gas”) securities fell in October 2004, the defendants disclosed customer attrition figures to the public and made it clear that Star Gas’s Business Improvement Plan (the “BIP”) was facing significant challenges.1 For example, in a *644July 2004 press release, defendant Sevin described the implementation of the BÍP as “particularly challenging” and disclosed that Star Gas’s operating income had decreased by approximately $4 million due in part to the effect of “an approximate 4% net customer loss resulting from both high energy prices and diminished service levels ... associated with the initial stages of [the BIP].” To the extent that any of Sevin’s earlier positive statements about the progress of the BIP could have misled investors, Sevin’s July 2004 disclosures defeat the claim that the October 2004 announcement “belatedly revealed” that Star Gas suffered high customer attrition principally related to the BIP, causing security prices to fall. Accordingly, the Complaint fails to adequately allege that any of Sev-in’s early positive statements concealed something from the market that, when disclosed in October 2004, caused the fall in securities prices. See Lentell v. Merrill Lynch & Co., 396 F.3d 161, 173 (2d Cir. 2005).

Further, although Sevin’s July 2004 disclosure also included positive statements about the BIP, including that “we are beginning to see many of the operational and customer satisfaction benefits originally anticipated” and that he was optimistic “because we have a company under control,” there is no “substantial likelihood” that a “reasonable investor would have considered [these statements] significant in making investment decisions.” Ganino v. Citizens Utils. Co., 228 F.3d 154, 161-62 (2d Cir. 2000) (internal quotation marks omitted). Sevin’s positive statements about the BIP’s present stability were sufficiently vague and generalized that no reasonable investor would have relied upon them, particularly when coupled with Sevin’s concurrent disclosures about the BIP’s problems to date.2 As to Sevin’s forward-looking statements, the Complaint fails to allege facts supporting the conclusion that Sevin made optimistic statements in bad faith or without a reasonable basis. See San Leandro Emergency Med. Group Profit Sharing Plan v. Philip Morris Cos., 75 F.3d 801, 813 (2d Cir. 1996). Because Sevin’s statements constitute mere “expressions of puffery and corporate optimism,” they “do not give rise to securities violations.” Rombach v. Chang, 355 F.3d 164, 174 (2d Cir. 2004).

We conclude also that the district court did not abuse its discretion in dismissing the Complaint with prejudice, despite plaintiffs-appellants’ footnote request in their opposition brief for leave to amend if the district court “deems the claims against Defendants insufficiently pleaded.” See In re Tamoxifen Citrate Antitrust Litig., 466 F.3d 187, 220 (2d Cir. 2006) (“It is within the court’s discretion to deny leave to amend implicitly by not addressing the request when leave is requested informally in a brief filed in opposition to a motion to dismiss.”). Nor did the district court abuse its discretion in denying plaintiffs-appellants’ motion to modify the judgment, see Gorman v. Consol. Edison Corp., 488 F.3d 586, 592 (2d Cir. 2007) (“Generally, we review a district court’s denial of a motion to amend under the abuse of discretion standard.”), even assuming arguendo the applicability of the *645liberal Rule 15(a) standard. See In re Star Gas Sec. Litig., 241 F.R.D. 428, 433 (D.Conn. 2007) (denying plaintiffs’ motion “even taking into account the liberal policy of Rule 15(a)” (internal quotation marks omitted)). The district court gave plaintiffs-appellants the opportunity to amend the Complaint after a pre-motion telephone conference where the defendants described them arguments in favor of dismissal. Plaintiffs-appellants declined to do so. Thereafter, plaintiffs-appellants did not move to amend the Complaint after the defendants filed their briefs in support of dismissal. Although plaintiffs-appellants informally requested leave to amend in their motion papers, they did not submit proposed amendments or otherwise indicate how they would correct any deficiencies in the Complaint. Under these circumstances, it was within the district court’s discretion to dismiss the Complaint with prejudice. See Porat v. Lincoln Towers Cmty. Ass’n, 464 F.3d 274, 276 (2d Cir. 2006) (per curiam) (rejecting “a broad rule to the effect that, in the case of a counseled plaintiff, abuse of discretion will be found and the case remanded whenever a district court fails to provide for repleading”).

For the foregoing reasons, the judgment of the district court dismissing the Complaint and denying the post-judgment motion to amend the Complaint is AFFIRMED.