Optimal investment strategy for asset-liability management under the Heston model. (4th May 2019)

• Record Type: Journal Article
• Authors: Pan, Jian; Hu, Shengzhou; Zhou, Xiangying
• Is Part Of: Optimization. Volume 68:Number 5(2019)
• Page Start: 895
• Page End: 920
• Publication Date: 2019-05-04
• Subjects: Asset-liability management -- Heston model -- exponential utility function -- Hamilton–Jacobi–Bellman equation -- optimal investment strategy; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1561691
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: This paper focuses on an asset-liability management problem for an investor who can invest in a risk-free asset and a risky asset whose price process is governed by the Heston model. The objective of the investor is to find an optimal investment strategy to maximize the expected exponential utility of the surplus process. By using the stochastic control method and variable change techniques, we obtain a closed-form solution of the corresponding Hamilton–Jacobi–Bellman equation. We also develop a verification theorem without the usual Lipschitz assumptions which can ensure that this closed-form solution is indeed the value function and then derive the optimal investment strategy explicitly. Finally, we provide numerical examples to show how the main parameters of the model affect the optimal investment strategy.