Pith Number

pith:RGXDALKT

pith:2026:RGXDALKTSLDC3LWB7DIXH6WZMU

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On the optimal portfolio problem with partial information and related mean field games with relative performance criteria

Panagiotis Souganidis, Thaleia Zariphopoulou

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.

arxiv:2605.14519 v1 · 2026-05-14 · math.OC

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Record completeness

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

61 extracted · 61 resolved · 1 Pith anchors

[1] 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 2003

[2] 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 2022

[3] Bain, A. and D. Crisan, Fundamentals of stochastic filtering, Stochastic Modeling and Applied Probability Series, Springer Verlag, 2009 2009

[4] Baltas, N., The impact of crowding in alternative risk premia investing, Financial Analysts Journal, 75(3), 89-104, 2019 2019

[5] 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 2021

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:06.091429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89ae302d5392c62daec1f8d173fad96511f0d431275d339bb4c158feb8ffeca4

Aliases

arxiv: 2605.14519 · arxiv_version: 2605.14519v1 · doi: 10.48550/arxiv.2605.14519 · pith_short_12: RGXDALKTSLDC · pith_short_16: RGXDALKTSLDC3LWB · pith_short_8: RGXDALKT

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RGXDALKTSLDC3LWB7DIXH6WZMU \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 89ae302d5392c62daec1f8d173fad96511f0d431275d339bb4c158feb8ffeca4

Canonical record JSON

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    "abstract_canon_sha256": "d4217c9240e8cfd4db3c03a4604cee64fa29404f17404a74cdbff1901348fcc4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-14T08:03:16Z",
    "title_canon_sha256": "bf352dc2b0ae751f05945f70b46bb3b70a5ef7a610440d41b0d2ed36a9ea0ace"
  },
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    "id": "2605.14519",
    "kind": "arxiv",
    "version": 1
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}