Equilibrium Portfolio Selection under Utility-Variance Analysis of Log Returns in Incomplete Markets
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918225144446976 |
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| author | Cao, Yue Liang, Zongxia Wang, Sheng Yu, Xiang |
| author_facet | Cao, Yue Liang, Zongxia Wang, Sheng Yu, Xiang |
| contents | This paper investigates a time-inconsistent portfolio selection problem in the incomplete mar ket model, integrating expected utility maximization with risk control. The objective functional
balances the expected utility and variance on log returns, giving rise to time inconsistency and
motivating the search of a time-consistent equilibrium strategy. We characterize the equilibrium
via a coupled quadratic backward stochastic differential equation (BSDE) system and establish
the existence theory in two special cases: (i)the two Brownian motions driven the price dynamics
and the factor process are independent with $ρ= 0$; (ii) the trading strategy is constrained to
be bounded. For the general case with correlation coefficient $ρ\neq 0$, we introduce the notion
of an approximate time-consistent equilibrium. Employing the solution structure from the
equilibrium in the case $ρ= 0$, we can construct an approximate time-consistent equilibrium in
the general case with an error of order $O(ρ^2)$. Numerical examples and financial insights are
also presented based on deep learning algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05861 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equilibrium Portfolio Selection under Utility-Variance Analysis of Log Returns in Incomplete Markets Cao, Yue Liang, Zongxia Wang, Sheng Yu, Xiang Portfolio Management Optimization and Control This paper investigates a time-inconsistent portfolio selection problem in the incomplete mar ket model, integrating expected utility maximization with risk control. The objective functional balances the expected utility and variance on log returns, giving rise to time inconsistency and motivating the search of a time-consistent equilibrium strategy. We characterize the equilibrium via a coupled quadratic backward stochastic differential equation (BSDE) system and establish the existence theory in two special cases: (i)the two Brownian motions driven the price dynamics and the factor process are independent with $ρ= 0$; (ii) the trading strategy is constrained to be bounded. For the general case with correlation coefficient $ρ\neq 0$, we introduce the notion of an approximate time-consistent equilibrium. Employing the solution structure from the equilibrium in the case $ρ= 0$, we can construct an approximate time-consistent equilibrium in the general case with an error of order $O(ρ^2)$. Numerical examples and financial insights are also presented based on deep learning algorithms. |
| title | Equilibrium Portfolio Selection under Utility-Variance Analysis of Log Returns in Incomplete Markets |
| topic | Portfolio Management Optimization and Control |
| url | https://arxiv.org/abs/2511.05861 |