Robust optimal asset-liability management with mispricing and stochastic factor market dynamics

Ning Wang, Yumo Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

This paper investigates a robust optimal asset-liability management problem under an expected utility maximization criterion. More specifically, the manager is concerned about the potential model uncertainty and aims to seek the robust optimal investment strategies. We incorporate an uncontrollable random liability described by a generalized drifted Brownian motion. Also, the manager has access to an incomplete financial market consisting of a risk-free asset, a market index with potentially path-dependent, time-varying risk premium and volatility, and a pair of mispriced stocks. The market dynamics are assumed to rely on an affine-form, square-root factor process and the price error is modeled by a co-integrated system. We adopt a backward stochastic differential equation approach hinging on the martingale optimality principle to solve this non-Markovian robust control problem. Closed-form expressions for the robust optimal investment strategies, the probability perturbation process under the well-defined worst-case scenario and the corresponding value function are derived. The admissibility of the robust optimal controls is verified under some technical conditions. Finally, we perform some numerical examples to illustrate the effects of model parameters on the robust investment strategies and draw some economic interpretations from these results.

Original languageEnglish
Pages (from-to)251-273
Number of pages23
JournalInsurance: Mathematics and Economics
Volume113
DOIs
Publication statusPublished - Nov 2023
Externally publishedYes

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