Dual control Monte-Carlo method for tight bounds of value function under Heston stochastic volatility model

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Title: Dual control Monte-Carlo method for tight bounds of value function under Heston stochastic volatility model
Authors: Ma, J
Li, W
Zheng, H
Item 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.
Issue Date: 23-Jul-2019
Date of Acceptance: 19-Jul-2019
URI: http://hdl.handle.net/10044/1/72349
DOI: http://doi.org/10.1016/j.ejor.2019.07.041
ISSN: 0377-2217
Publisher: Elsevier BV
Journal / Book Title: European Journal of Operational Research
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/
Keywords: MD Multidisciplinary
Operations Research
Publication Status: Published online
Embargo Date: 2021-07-23
Online Publication Date: 2019-07-23
Appears in Collections:Financial Mathematics
Mathematics



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