Application of the integro-differential equation in the calculation of probability of losses of the death guarantee program of an insurance company

The chance of bankruptcy for the first time in an insurance company indicates the possibility of bankruptcy of an insurance company. This is indicated by the negative value of the surplus function or which means the company can no longer bear the burden of claims in the next period. The number of claims that occur in a certain period of time can be viewed as data with a random distribution of variables, which theoretically can be calculated using a statistical approach with the concept of ruin probability. In this study, the probability of loss function is calculated by analyzing the surplus function at a certain time. This concept can be used not only to calculate bankruptcy in its entirety, but also can be used to predict the loss of an insurance program at a certain time. The value of the probability function of bankruptcy risk is determined by using a mathematical model developed based on the concept of integro-differential equations, which is used as a reference to determine what the company will face in the future. In the simulation, the loss probability function of the Death Insurance Program at insurance companies against surplus value based on 2019 data, shows that the greater the surplus value, the smaller the loss probability function.