TY - JOUR

T1 - Robust optimal asset-liability management with mispricing and stochastic factor market dynamics

AU - Wang, Ning

AU - Zhang, Yumo

N1 - Publisher Copyright: © 2023 Elsevier B.V.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Asset-liability management

KW - Backward stochastic differential equation

KW - Mispricing

KW - Model ambiguity

KW - Stochastic factor

UR - http://www.scopus.com/inward/record.url?scp=85171568765&partnerID=8YFLogxK

U2 - 10.1016/j.insmatheco.2023.09.001

DO - 10.1016/j.insmatheco.2023.09.001

M3 - Journal article

AN - SCOPUS:85171568765

VL - 113

SP - 251

EP - 273

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

SN - 0167-6687

ER -