Assessment of the insurance company with Laplace transform

Abstract

A model of assessment of the solvency of the insurance company is designed in the paper. For a wide class of tasks it is shown that obtaining an analytical expression for the function of payment magnitude distribution is possible only with the use of numerical methods, including algorithm due to Dufresne and Gerber. It is indicated that if the value of payments has an exponential distribution, there is a possibility of obtaining an analytic solution of the problem by means of inverse Laplace transforms. The probability of stable operation of the insurance company is discovered, as well as a graphical representation of the results depending on the distribution parameters is achieved.