G-expected utility maximization with ambiguous equicorrelation

Abstract

This paper studies a class of expected utility maximization problems 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 consider more than two ambiguous parameters that could be interactive in general. We manage to derive an analytical solution to the robust stochastic controls under an ambiguous two-block equicorrelated structure via the solution to a system of polynomial equations. The results have significant implications for the investment and reinsurance problems among many others.

Keywords:

• Ambiguous equicorrelation
• G-expectation
• Expected utility maximization
• Hamilton–Jacobi–Bellman–Isaacs equation
• Worst-case optimization
• System of polynomial equations

JEL Classification:

• D81 – Information
• Knowledge
• and Uncertainty – Criteria forDecision-Making under Risk and Uncertainty
• G11 – General Financial Markets –Portfolio Choice/Investment Decisions
• C32 – Multiple Variables – Time-Series Models
• C55 – Econometric Modeling – Large Data Sets: Modeling and Analysis
• C61 –Mathematical Methods – Optimization Techniques

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was partially supported by Ministry of Education, Singapore, AcRF Tier 2 grant (Reference No: MOE2017-T2-1-044).