Research On Bankruptcy Problem Of Credit Risk Model Based On Default

In this paper, we combine the credit risk in financial engineering and the bankruptcy theory of the insurance actuarial, and study the bankruptcy of the company with the characteristics of the transfer of credit. Which different with the general credit risk model is that this paper not only consider the case of default, simulates the transfer between the company’s credit rating by using a time homogeneous with absorbing state of the Markov chain and it’s quality which is called “no aftereffect”, but also in order to fit more practical,the model under interest rates and interest rate obey independent identically distributed are studied respectively.Firstly, the paper introduces the Markov chain with discrete parameters, and introduces the general credit risk model with finite discrete time, and elaborated the related definition and conclusion.Secondly, the paper have established a credit risk model with default situation, assume that transfer between the firm’s credit rating is obeyed a time homogeneous with absorbing state of the Markov chain, and make full use of the Markov chain’s "no aftereffect”,calculating the survival probability, the breaking moments of the distribution, the distribution of the instantaneous surplus and bankruptcy bankruptcy instantaneous balance distribution of this model.And then, the paper established the credit risk model with constant interest rate that is based on the case of default, and uses the method of recursion to obtain the survival probability, the distribution of the ruin time, the instantaneous surplus distribution and the instantaneous balance distribution of the ruin of the model.Finally, in order to make the model more practical, the paper have considered the interest rate obey independent identically distributed, the distribution of the survival probability, the distribution of the ruin time, the instantaneous surplus distribution before ruin, and the instantaneous distribution of the ruin time of this model are also calculated.