G-Expected Utility Maximization with Ambiguous Equicorrelation

Forthcoming in Quantitative Finance

27 Pages Posted: 15 Dec 2018 Last revised: 1 Jun 2020

See all articles by Chi Seng Pun

Chi Seng Pun

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

Date Written: May 28, 2020

Abstract

This paper studies the expected utility maximization problem with respect to a controlled state process with multiple noises, whose pairwise correlations are equal and ambiguous. Using the G-expectation theory, we solve for the robust stochastic controls explicitly from a Hamilton-Jacobi-Bellman-Isaacs equation and deduce a robust choice of the equicorrelation coefficient. We also generalize the results to a block equicorrelation structure, where we strike the balance between efficiency and tractability. Although we face with many ambiguous parameters that may be interactive in the general case, we manage to derive an analytical solution to the robust stochastic controls under the ambiguity of a two-block equicorrelated structure via the solution to a system of polynomial equations. The results have significant implications to the investment and reinsurance problems among many others.

Keywords: ambiguous equicorrelation, G-expectation, expected utility maximization, Hamilton-Jacobi-Bellman-Isaacs equation, explicit solution, system of polynomial equations

Suggested Citation

Pun, Chi Seng, G-Expected Utility Maximization with Ambiguous Equicorrelation (May 28, 2020). Forthcoming in Quantitative Finance, Available at SSRN: https://ssrn.com/abstract=3276001 or http://dx.doi.org/10.2139/ssrn.3276001

Chi Seng Pun (Contact Author)

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences ( email )

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21 Nanyang Link
Singapore, 637371
Singapore
(+65) 6513 7468 (Phone)

HOME PAGE: http://personal.ntu.edu.sg/cspun/

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