Finite-time stability and optimal control for stochastic credit risk contagion model with sentiment

Abstract

Counterparty sentiment and major uncertain factors always affect credit risk contagion in credit risk transfer (CRT) market. In order to effectively analyze credit risk contagion, this paper proposes a stochastic credit risk contagion model considering sentiments, in which the stochasticity is driven by Lévy process. Based on the Lyapunov function method, sufficient condition of finite-time stability is derived. The impacts of counterparty sentiment and Lévy process on credit risk contagion are analyzed. To effectively control credit risk contagion, the stochastic credit risk control model is established, and the optimal control strategy is given by using Pontryagin’s maximum principle. Numerical simulating results show the correctness and effectiveness of the theory.