TY - JOUR

T1 - Non-zero-sum Stochastic Differential Games for Asset-Liability Management with Stochastic Inflation and Stochastic Volatility

AU - Zhang, Yumo

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

PY - 2024

Y1 - 2024

N2 - This paper investigates the optimal asset-liability management problems for two managers subject to relative performance concerns in the presence of stochastic inflation and stochastic volatility. The objective of the two managers is to maximize the expected utility of their relative terminal surplus with respect to that of their competitor. The problem of finding the optimal investment strategies for both managers is modeled as a non-zero-sum stochastic differential game. Both managers have access to a financial market consisting of a risk-free asset, a risky asset, and an inflation-linked index bond. The risky asset’s price process and uncontrollable random liabilities are not only affected by the inflation risk but also driven by a general class of stochastic volatility models embracing the constant elasticity of variance model, the family of state-of-the-art 4/2 models, and some path-dependent models. By adopting a backward stochastic differential equation (BSDE) approach to overcome the possibly non-Markovian setting, closed-form expressions for the equilibrium investment strategies and the corresponding value functions are derived under power and exponential utility preferences. Moreover, explicit solutions to some special cases of our model are provided. Finally, we perform numerical studies to illustrate the influence of relative performance concerns on the equilibrium strategies and draw some economic interpretations.

AB - This paper investigates the optimal asset-liability management problems for two managers subject to relative performance concerns in the presence of stochastic inflation and stochastic volatility. The objective of the two managers is to maximize the expected utility of their relative terminal surplus with respect to that of their competitor. The problem of finding the optimal investment strategies for both managers is modeled as a non-zero-sum stochastic differential game. Both managers have access to a financial market consisting of a risk-free asset, a risky asset, and an inflation-linked index bond. The risky asset’s price process and uncontrollable random liabilities are not only affected by the inflation risk but also driven by a general class of stochastic volatility models embracing the constant elasticity of variance model, the family of state-of-the-art 4/2 models, and some path-dependent models. By adopting a backward stochastic differential equation (BSDE) approach to overcome the possibly non-Markovian setting, closed-form expressions for the equilibrium investment strategies and the corresponding value functions are derived under power and exponential utility preferences. Moreover, explicit solutions to some special cases of our model are provided. Finally, we perform numerical studies to illustrate the influence of relative performance concerns on the equilibrium strategies and draw some economic interpretations.

KW - 60H30

KW - 91A15

KW - 93E20

KW - Asset-liability management

KW - Backward stochastic differential equation

KW - Non-zero-sum game

KW - Relative performance concerns

KW - Stochastic inflation

KW - Stochastic volatility

U2 - 10.1007/s11009-024-10072-3

DO - 10.1007/s11009-024-10072-3

M3 - Journal article

AN - SCOPUS:85185696585

VL - 26

SP - 1

EP - 47

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

SN - 1387-5841

IS - 1

M1 - 7

ER -