Ruin Probability Based On Risk Model With Special Capital Constraints

In financial insurance,the bankruptcy theory in insurance risk theory is a very important research topic,because it allows policy makers in insurance companies to predict the degree of risk of bankruptcy in advance,so research has its important theoretical and practical significance.In order to minimize the possibility of insurance company bankruptcy and allow shareholders to get rich returns on their investments.Some scholars have introduced the classic compound Poisson risk model by introducing orderly capital levels to simulate the solvency of insurance companies.When the earnings process is lower than the higher capital level,resulting in a larger claim size and without further disrupting the more so-called intermediate confidence(shareholder’s)level,shareholders only need to inject capital to restore the earnings process to saturation.On the other hand,if the confidence level is broken but the lower capital level is not destroyed,capital injection is no longer a viable method.Instead,insurance companies can borrow money from third-party companies,but need continuous premium income until the surplus process returns to a confidence level and can then be fully saturated through capital injections.If the surplus process breaks the lower capital level at any time,the company is considered "insolvent" and forced to stop trading and declare bankruptcy.In the above risk model,scholars convert the ruin probability of the classic risk model into a display expression of "probability of ruin" under special capital constraints,and under the assumption of exponentially distributed claims scale,they show the possibility of bankruptcy under capital constraints It is actually proportional to the classical ruin probability function.For example,when the higher level of capital is set to be larger,the value of the proportionality coefficient is smaller,so that the smaller the value of the probability of bankruptcy under the capital constraint,the greater the protection for the insurance company.It also shows that for a risk model with a general claim size distribution,the asymptotic result of the ruin probability is also proportional to the classic ruin probability function.Finally,in order to make the newly established model closer to reality,consider the constant dividend with capital constraints.When a certain level of capital is reached,the dividend paid to the company’s shareholders(complete dividends)is obtained.Explicit expression of the capital-constrained ruin probability.Through the numerical calculation and analysis of the new model,it is concluded that under special capital constraints,the impact of different capital levels,premium income and loan interest rates on the probability of bankruptcy has practical guidance for the actual operation of insurance companies.