Optimal portfolio choice with capital gains tax under Heston's stochastic volatility model

Qi Wang; Linyi Qian; Wei Wang; Qi Wang; Linyi Qian; Wei Wang

doi:10.3934/jimo.2026052

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 3: 1419-1439. doi: 10.3934/jimo.2026052

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Optimal portfolio choice with capital gains tax under Heston's stochastic volatility model

1.
College of Digital Technology and Engineering, Ningbo University of Finance and Economics, Ningbo, 315175, China
2.
School of Statistics, East China Normal University, Shanghai, 200062, China
3.
School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, China

Received: 14 November 2025 Revised: 28 January 2026 Accepted: 04 February 2026 Published: 25 February 2026
91G10, 93E20

In this paper, we studied optimal investment problems with capital gains tax. The price process of the risky asset was assumed to be governed by Heston's stochastic volatility model. Furthermore, the tax evasion behavior of investors was also considered in our model. However, investors will be punished when their tax evasion behaviors are noticed by the audit. By maximizing the expected utility of terminal wealth, the corresponding Hamilton-Jacobi-Bellman (HJB) equation was obtained by using the principle of stochastic dynamic programming. Then, we obtained analytical solutions of the optimal investment strategies by using the first-order optimality conditions and solving the HJB equations. Finally, some numerical results and economic explanations were provided to make further illustrations.
- capital gains tax,
- Heston's stochastic volatility model,
- optimal investment strategy
Citation: Qi Wang, Linyi Qian, Wei Wang. Optimal portfolio choice with capital gains tax under Heston's stochastic volatility model[J]. Journal of Industrial and Management Optimization, 2026, 22(3): 1419-1439. doi: 10.3934/jimo.2026052

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Abstract

In this paper, we studied optimal investment problems with capital gains tax. The price process of the risky asset was assumed to be governed by Heston's stochastic volatility model. Furthermore, the tax evasion behavior of investors was also considered in our model. However, investors will be punished when their tax evasion behaviors are noticed by the audit. By maximizing the expected utility of terminal wealth, the corresponding Hamilton-Jacobi-Bellman (HJB) equation was obtained by using the principle of stochastic dynamic programming. Then, we obtained analytical solutions of the optimal investment strategies by using the first-order optimality conditions and solving the HJB equations. Finally, some numerical results and economic explanations were provided to make further illustrations.

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