Ruin Probability In Two-dimentional Risk Model

This paper considers ruin problem of two-dimentional risk model.First,we extend the martingale approach and the theory about change of measure of the one-dimensional risk model to the two-dimensional risk model.Using the martingale approach and the theory about change of measure,the ruin probability of two-dimentional compound Poisson risk model is studied.Under the new measure,the risk process is still a two-dimentional compound Poisson risk process.And we get the expressions of the ruin probability.We obtain a Lundberg-type upper bound of the infinite-time ruin probability for two-dimentional risk model in two collaborating insurance companies.Then,we use the theory of minimal nonnegative solution.We obtain an iterative approach for the ruin probability of two-dimentional compound Poisson risk model based on the ruin time ?min.And we get an iterative approach for the ruin probability of the first company under the cooperation mechanism.Finally,the ruin probability of two-dimensional Sparre Andersen risk model with geometrical distributed inter-occurrence times is studied.An exponential martingale obtained by virtue of the extended generator to applied to the change of probability measure for this model.The adjustment coefficient is analyzed in polar coordinates in this model.Then we get the expressions of the ruin probability and obtain a Lundberg-type upper bound for the infinite-time ruin probability.