Equilibrium strategy in a non-performing loan securitization game with regime switching

Pin Wang; Guojing Wang; Yang Yang; Wanrong Mu; Pin Wang; Guojing Wang; Yang Yang; Wanrong Mu

doi:10.3934/jimo.2026025

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 1: 691-715. doi: 10.3934/jimo.2026025

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Research article

Equilibrium strategy in a non-performing loan securitization game with regime switching

1.
Center for Financial Engineering, Soochow University, Suzhou, 215006, China
2.
School of Mathematics and Statistics, Zaozhuang University, Zaozhuang, 277160, China
3.
School of Mathematics and Finance, Chuzhou University, Chuzhou, 239000, China

Received: 11 September 2025 Revised: 29 October 2025 Accepted: 11 November 2025 Published: 19 December 2025
91G30, 91A15

This paper investigates the equilibrium of a non-performing loan (NPL) securitization market characterized by strategic interactions between multiple banks and insurers. We develop a continuous-time framework in which the NPL recovery process is modeled by a Markov chain capturing stochastic macroeconomic regime shifts. Within this market, risk-averse banks and insurers—both represented by exponential utility preferences—seek to maximize their certainty-equivalent terminal wealth through optimal choices of securitization and guarantee ratios. Employing optimization techniques, we establish the equilibrium model and derive analytical, closed-form solutions for the equilibrium strategies as well as the endogenous insurance premium. Numerical experiments illustrate how equilibrium outcomes respond to key factors such as agents' risk aversion and macroeconomic transition probabilities, thereby validating the theoretical framework and offering a rigorous tool for practical decision-making and regulatory evaluation.
- non-performing loans,
- securitization,
- equilibrium game model,
- diffusion approximation,
- regime-switching
Citation: Pin Wang, Guojing Wang, Yang Yang, Wanrong Mu. Equilibrium strategy in a non-performing loan securitization game with regime switching[J]. Journal of Industrial and Management Optimization, 2026, 22(1): 691-715. doi: 10.3934/jimo.2026025

Related Papers:

Abstract

This paper investigates the equilibrium of a non-performing loan (NPL) securitization market characterized by strategic interactions between multiple banks and insurers. We develop a continuous-time framework in which the NPL recovery process is modeled by a Markov chain capturing stochastic macroeconomic regime shifts. Within this market, risk-averse banks and insurers—both represented by exponential utility preferences—seek to maximize their certainty-equivalent terminal wealth through optimal choices of securitization and guarantee ratios. Employing optimization techniques, we establish the equilibrium model and derive analytical, closed-form solutions for the equilibrium strategies as well as the endogenous insurance premium. Numerical experiments illustrate how equilibrium outcomes respond to key factors such as agents' risk aversion and macroeconomic transition probabilities, thereby validating the theoretical framework and offering a rigorous tool for practical decision-making and regulatory evaluation.

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