Mean-variance portfolio selection in jump-diffusion model under no-shorting constraint: A viscosity solution approach
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909218215297024 |
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| author | Shi, Xiaomin Xu, Zuo Quan |
| author_facet | Shi, Xiaomin Xu, Zuo Quan |
| contents | This paper concerns a continuous time mean-variance (MV) portfolio selection problem in a jump-diffusion financial model with no-shorting trading constraint. The problem is reduced to two subproblems: solving a stochastic linear-quadratic (LQ) control problem under control constraint, and finding a maximal point of a real function. Based on a two-dimensional fully coupled ordinary differential equation (ODE), we construct an explicit viscosity solution to the Hamilton-Jacobi-Bellman equation of the constrained LQ problem. Together with the Meyer-Itô formula and a verification procedure, we obtain the optimal feedback controls of the constrained LQ problem and the original MV problem, which corrects the flawed results in some existing literatures. In addition, closed-form efficient portfolio and efficient frontier are derived. In the end, we present several examples where the two-dimensional ODE is decoupled. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03709 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mean-variance portfolio selection in jump-diffusion model under no-shorting constraint: A viscosity solution approach Shi, Xiaomin Xu, Zuo Quan Optimization and Control Mathematical Finance Portfolio Management This paper concerns a continuous time mean-variance (MV) portfolio selection problem in a jump-diffusion financial model with no-shorting trading constraint. The problem is reduced to two subproblems: solving a stochastic linear-quadratic (LQ) control problem under control constraint, and finding a maximal point of a real function. Based on a two-dimensional fully coupled ordinary differential equation (ODE), we construct an explicit viscosity solution to the Hamilton-Jacobi-Bellman equation of the constrained LQ problem. Together with the Meyer-Itô formula and a verification procedure, we obtain the optimal feedback controls of the constrained LQ problem and the original MV problem, which corrects the flawed results in some existing literatures. In addition, closed-form efficient portfolio and efficient frontier are derived. In the end, we present several examples where the two-dimensional ODE is decoupled. |
| title | Mean-variance portfolio selection in jump-diffusion model under no-shorting constraint: A viscosity solution approach |
| topic | Optimization and Control Mathematical Finance Portfolio Management |
| url | https://arxiv.org/abs/2406.03709 |