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.