Non-zero-sum Stochastic Differential Games for Asset-Liability Management with Stochastic Inflation and Stochastic Volatility
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Non-zero-sum Stochastic Differential Games for Asset-Liability Management with Stochastic Inflation and Stochastic Volatility. / Zhang, Yumo.
I: Methodology and Computing in Applied Probability, Bind 26, Nr. 1, 7, 2024, s. 1-47.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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 -
ID: 384875293