Research on the Optimal Investment Strategy with Jumps When Risks Cannot Be Hedged
Vol. 5 (2025): 2025 3rd International Conference on the Sociology of the Global Economy, Education, Arts and Humanities (GEEAH 2025)
Received: 2026-05-23
Accepted: 2026-05-23
Published: 2026-05-23
Abstract
The problem of the optimal investment strategy has always been a key research content in modern finance. Since stock prices in real financial markets often experience jumps, and the randomness of investors' labor income contributes to risks that cannot be completely hedged, it is necessary to consider these factors in investment strategy design. This paper studies the continuous-time dynamic mean-variance portfolio selection problem when the risk is not hedged. It is assumed that the price of risky assets follows a jump-diffusion process. The investor's goal is to minimize the variance of the wealth at the terminal time under the condition of a given expected terminal wealth. By solving the corresponding Hamilton-Jacobi-Bellman equation of the model, the viscosity solution of the optimal investment strategy is obtained. The results show that the jump factors in the price process and the unhedged risk have an impact on the optimal investment strategy that cannot be ignored.
Keywords
References
[1] Y. Guo, X. B. Shu, F. Xu, and C. Yang, “HJB equation for optimal control system with random impulses,” Optim., vol. 73, no. 4, pp. 1303–1327, 2024, doi: 10.1080/02331934.2022.2154607.
[2] R. C. Merton, “Optimum consumption and portfolio rules in a continuous-time model,” in Stochastic Optim. Models Finance, New York, NY, USA: Academic Press, 1975, pp. 621–661, doi: 10.1016/B978-0-12-780850-5.50052-6.
[3] W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, vol. 1. New York, NY, USA: Springer Sci. & Bus. Media, 2012. ISBN: 9781461263807.
[4] M. Longo and A. Mainini, “Learning and portfolio decisions for CRRA investors,” Int. J. Theor. Appl. Finance, vol. 19, no. 3, p. 1650018, 2016, doi: 10.1142/S0219024916500187.
[5] X. Liu, Z. Cai, and Z. Gao, “The growth of a single rising bubble in viscous solution and the resulting volatile removal,” Chem. Eng. Sci., vol. 293, p. 120062, 2024, doi: 10.1016/j.ces.2024.120062.
[6] Q. B. Yin, X. B. Shu, Y. Guo, and Z. Y. Wang, “Optimal control of stochastic differential equations with random impulses and the Hamilton–Jacobi–Bellman equation,” Optim. Control Appl. Methods, vol. 45, no. 5, pp. 2113–2135, 2024, doi: 10.1002/oca.3139.
Copyright and License
Published in2026-05-23 15:22:12
DOI 10.70088/mx65ey07
Creative Commons
Copyright: © 2025 by the authors.
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Copyright © The Author(s), 2025. Published by GEEAH 2025
Journal Information
- Vol. 5 (2025): 2025 3rd International Conference on the Sociology of the Global Economy, Education, Arts and Humanities (GEEAH 2025)
- 2026-05-23
- ISSN: (Print) 3078-770X/ (Online) 3078-7718
- Journal Homepage