Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization
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 opt...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/3399493 |
| _version_ | 1797373113312215040 |
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| author | Lei Hu |
| author_facet | Lei Hu |
| author_sort | Lei Hu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T18:45:42Z |
| format | Article |
| id | doaj.art-17d987292b9c41ec89bef504ece24739 |
| institution | Directory Open Access Journal |
| issn | 2314-4785 |
| language | English |
| last_indexed | 2024-03-08T18:45:42Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj.art-17d987292b9c41ec89bef504ece247392023-12-29T00:00:52ZengHindawi LimitedJournal of Mathematics2314-47852023-01-01202310.1155/2023/3399493Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio OptimizationLei Hu0School of MathematicsIn 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.http://dx.doi.org/10.1155/2023/3399493 |
| spellingShingle | Lei Hu Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization Journal of Mathematics |
| title | Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization |
| title_full | Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization |
| title_fullStr | Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization |
| title_full_unstemmed | Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization |
| title_short | Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization |
| title_sort | application of asymptotic analysis of a high dimensional hjb equation to portfolio optimization |
| url | http://dx.doi.org/10.1155/2023/3399493 |
| work_keys_str_mv | AT leihu applicationofasymptoticanalysisofahighdimensionalhjbequationtoportfoliooptimization |