Abstarct: In today's economy, mathematical finance plays an important role in predicting precise models for the future of investment in different ‏‎departments‎. Especially in the financial markets, it's quite possible to touch this effect in the past and now. In fact, financial mathematics determines the risk and rate of return on capital.‎ ‎ Today, insurance companies have an important role in investing in different sectors of society (whether social or economic). Among them, we can mention issues such as health, industry, commerce, etc.‎ ‎ In this dissertation, we first outline the definitions of the fundamentals, as well as the definitions of the capital of the insurance company, the premium and the probability of bankruptcy, and then examine the results. Using the results we present a method for obtaining the risk of the insurance company. In fact, baxsed on the boundary value problem, we use Green's method to develop solutions to the risk level of the insurance company.‎ ‎