{"paper":{"title":"On the optimal portfolio problem with partial information and related mean field games with relative performance criteria","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Partial information on stock drift allows closed-form optimal portfolios for general utilities, with mean-field relative performance games reducing to a nonlocal quasilinear PDE.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Panagiotis Souganidis, Thaleia Zariphopoulou","submitted_at":"2026-05-14T08:03:16Z","abstract_excerpt":"We study optimal portfolio choice models in markets with partial information about the stock's drift. We solve the single agent problem for general utilities using a new approach that yields regularity of the value function and closed form expressions for the optimal processes. We consider a N player game in which players interact through the law of peer's wealth and study its mean field limit. This leads to a a game with field equilibrium. We analyze the cases of separable couplings and general utilities, and represent the value of the game as a compilation of the single player problem and a "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We solve the single agent problem for general utilities using a new approach that yields regularity of the value function and closed form expressions for the optimal processes. [...] represent the value of the game as a compilation of the single player problem and a function solving a non local quasilinear pde in the space of measures.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The partial information structure on the stock drift (typically a hidden process) and the specific separable or average-based couplings allow the mean-field limit to exist and the nonlocal quasilinear PDE to admit sufficiently regular solutions for the value representation to hold.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Solves portfolio optimization under partial drift information with closed forms for general utilities and represents mean-field game values with relative performance via single-agent problems plus nonlocal PDE solutions in measure space.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Partial information on stock drift allows closed-form optimal portfolios for general utilities, with mean-field relative performance games reducing to a nonlocal quasilinear PDE.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0e75b6d840fc316226aee429b0182b30ad30c7ffc93a51c0344b7953ecda6510"},"source":{"id":"2605.14519","kind":"arxiv","version":1},"verdict":{"id":"d5de0b63-8524-4fdf-89b4-cb8b43cd69e3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:38:11.707438Z","strongest_claim":"We solve the single agent problem for general utilities using a new approach that yields regularity of the value function and closed form expressions for the optimal processes. [...] represent the value of the game as a compilation of the single player problem and a function solving a non local quasilinear pde in the space of measures.","one_line_summary":"Solves portfolio optimization under partial drift information with closed forms for general utilities and represents mean-field game values with relative performance via single-agent problems plus nonlocal PDE solutions in measure space.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The partial information structure on the stock drift (typically a hidden process) and the specific separable or average-based couplings allow the mean-field limit to exist and the nonlocal quasilinear PDE to admit sufficiently regular solutions for the value representation to hold.","pith_extraction_headline":"Partial information on stock drift allows closed-form optimal portfolios for general utilities, with mean-field relative performance games reducing to a nonlocal quasilinear PDE."},"references":{"count":61,"sample":[{"doi":"","year":2003,"title":"Agarwal, V., Daniel N.D. and N.Y. Naik, Flows, performance and manage- rial incentives in hedge funds. In: EFA 2003, annual conference, paper No. 501, 2003","work_id":"26cacc20-31a6-402d-8ad3-d94b46493190","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Anthropelos, M., Geng, T. and T. Zariphopoulou, Competition in fund management under forward performance criteria, SIAM Journal on Finan- cial Mathematics, 13(4), 2022, 1271-1320","work_id":"d6ab3cab-5eab-4531-9a96-af9d6f5548b2","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"Bain, A. and D. Crisan, Fundamentals of stochastic filtering, Stochastic Modeling and Applied Probability Series, Springer Verlag, 2009","work_id":"0954f7e4-cfa3-47f7-8d1a-e5962f62cb19","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Baltas, N., The impact of crowding in alternative risk premia investing, Financial Analysts Journal, 75(3), 89-104, 2019","work_id":"8669eca1-be02-4081-a36b-e8cda3bf1da4","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"Barroso, P., Edelen, R.M. and P. Karehnke, Crowding and tail risk in mo- mentum returns, Journal of Financial and Quantitative Analysis, 57(4), 2021","work_id":"52bbb3f1-cc44-450a-b457-2c05e1ad5f79","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":61,"snapshot_sha256":"e860be64c81af9afc66bd400f09dddf83ab75b1a1491de03861095feed0ea354","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"541d5542887289b735eb4b89da1237b8e123ef6273eea3e088d6aec67c985fdc"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}