Dual control Monte-Carlo method for tight bounds of value function under Heston stochastic volatility model
File(s)
Accepted version
Author(s)
Ma, Jingtang
Li, Wenyuan
Zheng, Harry
Type
Journal Article
Abstract
The aim of this paper is to study the fast computation of the lower and upper bounds on the value function for utility maximization under the Heston stochastic volatility model with general utility functions. It is well known there is a closed form solution to the HJB equation for power utility due to its homothetic property. It is not possible to get closed form solution for general utilities and there is little literature on the numerical scheme to solve the HJB equation for the Heston model. In this paper we propose an efficient dual control Monte-Carlo method for computing tight lower and upper bounds of the value function. We identify a particular form of the dual control which leads to the closed form upper bound for a class of utility functions, including power, non-HARA and Yaari utilities. Finally, we perform some numerical tests to see the efficiency, accuracy, and robustness of the method. The numerical results support strongly our proposed scheme.
Date Issued
2020-01-16
Date Acceptance
2019-07-19
Citation
European Journal of Operational Research, 2020, 280 (2), pp.428-440
ISSN
0377-2217
Publisher
Elsevier BV
Start Page
428
End Page
440
Journal / Book Title
European Journal of Operational Research
Volume
280
Issue
2
Copyright Statement
© 2019 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Identifier
https://www.sciencedirect.com/science/article/pii/S0377221719306058?via%3Dihub
Subjects
Social Sciences
Science & Technology
Technology
Management
Operations Research & Management Science
Business & Economics
Utility maximization
Heston stochastic volatility model
Dual control Monte-Carlo method
Tight lower and upper bounds
Non-HARA and Yaari utilities
UTILITY MAXIMIZATION
EXPLICIT SOLUTION
ASSET ALLOCATION
INVESTMENT
OPTIONS
Operations Research
Publication Status
Published
Date Publish Online
2019-07-23