Dual control Monte Carlo method for tight bounds of value function under Heston stochastic volatility model release_4syer75t4fft7nuc5xam7tt3z4

by Jingtang Ma, Wenyuan Li, Harry Zheng

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2017  

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 of 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 Yarri 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.
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Date   2017-10-28
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arXiv  1710.10487v1
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