Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization

Lei Hu and Nan-Jing Huang

Journal of Mathematics, 2023, vol. 2023, 1-8

Abstract: In this paper, we consider a portfolio optimization problem where the wealth consists of investing into a risky asset with a slow mean-reverting volatility and receiving an uncontrollable stochastic cash flow under the exponential utility. The Hamilton–Jacobi–Bellman equation formulated from the optimal investment problem is a high-dimensional nonlinear partial differential equation and difficult to find its analytical or numerical solutions. The paper provides a tractable asymptotic approach which treats the initial problem as a perturbation around the constant volatility problem. In this paper, we present a formal derivation of asymptotic approximation and prove the accuracy of the value function. Moreover, an illustrative example is provided to assess our approximate strategy and value function.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:3399493

DOI: 10.1155/2023/3399493

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