{"paper":{"title":"Weight functions and log-optimal investment portfolios","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"I. Stuhl, M. Kelbert, Y. Suhov","submitted_at":"2015-05-06T17:19:24Z","abstract_excerpt":"Following the paper by Algoet--Cover (1988), we analyse log-optimal portfolios where return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, logarithmic growth rate is a supermartingale, and (B) the optimal (martingale) investment strategy is a proportional betting; it does not depend on the form of the weight function, although the optimal rate does. The existence of an optimal investment strategy has been established earlier in a great generality by Kramkov--Schachermayer (2003) although our underlying assumptions are different."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01437","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}