Utility Maximization Under Endogenous Pricing

• 成果类型: Article; Early Access
• 署名作者: Nguyen, Thai; Stadje, Mitja
• 署名单位: Laval University; Ulm University; Ulm University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2023.0376
• 发表日期: 2026-04-03
• 关键词: utility maximization; permanent market impact; endogenous pricing; g-expectation; forward-backward sdes; Backward SPDEs; Optimal investment; quadratic bsdes; BACKWARD; portfolio; expectations; consumption; options; IMPACT; fbsdes; MODEL

摘要

We study the expected utility maximization problem of a large investor who is allowed to make transactions on tradable assets in an incomplete financial market with endogenous permanent market impacts. The asset prices are assumed to follow a nonlinear price curve quoted in the market as the utility indifference curve of a representative liquidity supplier. Using generalized subgradients, we show that optimality can be fully characterized via a system of coupled forward-backward stochastic differential equations (FBSDEs) that corresponds to a nonlinear backward stochastic partial differential equation (BSPDE). We show existence of solutions to the optimal investment problem and the FBSDEs in the case in which the driver function of the representative market maker grows at least quadratically or the utility function of the large investor grows at least quadratically or is exponential. Furthermore, we derive smoothness results for the existence of solutions of BSPDEs. Examples are provided when the market is complete, the driver is positively homogeneous or the utility function is exponential.grows atleast