By using of recursive relation,we further study some problem in discrete risk model,such as the ultimate probability of ruin describing the safety state of insurance company,the immediately surplus before ruin and the deficit at ruin,which depict the degree of severity of ruin.

Derives the last probability of ruin and Lundberg upper bound in the condition of initial surplus of the insurance company is u(u≥0) by a discretionary stopping and martingale.

This paper derives the explicit formulation solution of the last probability of ruin and approachable estimate on exponential distribution of claims in the condition of initial surplus of the insurance company is u(u≥0).

The ruin probability of double compound negative binomial risk model;

On ruin probability for a generalized Cox insurance risk model with perturbation;

The ruin probability of a bankrupt problem with deductible;

In this paper,we study the probability of ruin in risk model with two Cos processes perturbed by diffusion and risk model with two Poisson processes perturbed by diffusion on the assumption that the limit of ruin is variation.

By the way, some results about the distribution of the deficit at ruin and the probability of ruin are derived.

A Mathematical Model Analysis on the Impact of the Capital Adequacy Requirement on Bankruptcy Probability;

The upper boundary of bankruptcy probability is obtained with martingale approach,further considering the influence of claim number on insurance income and obtaining its improved model and re.

By the method of Monte Carlo simulation and polymeric risk model,the paper resolves and analyses the bankruptcy probability under different scenarios,finds that the initial reserve has a big influence on the bankruptcy probability in the beginning period,and the bankruptcy probability with different initial reserves in the limited period will gradually reach the ultimate bankruptcy probability.