Application Of Martingale Analysis To The Cox Risk Model

The Martingale theory is a stochastic process front theory,Many years not only in the random process and its branch of mathematics occupy an important position in the,At the same time are being infiltrated to some other branch of mathematics,formation of some new research branch.In contemporary international insurance market , Investment in the insurance industry not only become the fulcrum of the normal operation,At the same time is considered an essential point of profit growth,The lifeblood of the modern insurance industry.At the same time use of reinsurance to spread risk,Through the signing of reinsurance contracts,insurers can actively and boldly doing business,Underwriting the risk beyond their own capabilities,Increase revenue,into account the role of these factors,This paper studies the interest rate with the investment income and reinsurance integrated Cox risk model of the probability of bankruptcy.First,In the original model based on the,Application of martingale convergence theory and the theory of stopping time integrated Cox risk model is still the ultimate ruin probability to meet the Lundberg inequality. And discussed the most simple form of the above models:Integrated Risk Model Homogeneous Poisson, Given the adjustment coefficient of the model existence theorem, So that the upper bound of ruin probability more perfect expression.Second, The introduction of Markov jump process, Application of martingale and vector of the relevant theory, Studied the Cox Markov environment, a comprehensive risk model the ultimate ruin probability, The model obtained the final expression for the upper bound of the probability of bankruptcy.Last, This article will use the sas software risk model to simulate, Obvious effect.