CALCULATION OF THE ULTIMATE RUIN PROBABILITY USING LAPLACE TRANSFORM

Abstract

Estimation of ruin probability is very important in insurance companies. Estimation used to anticipate the possibility of losses that may arise due to risks the unexpected events. In this thesis, the calculation of ruin probability using the Laplace transforms through the calculation of survival probability is discussed with Exponential and Gamma distribution. The numerical results from the three example cases of probability distribution functions show that the ruin probability depend on initial surplus. When initial surplus increase then the ruin probability decrease. This surplus is derived from the reserves of the initial surplus plus a premium amount received by the company multiplied by the number of insurance customers, then reduced by the number of claims issued. The insurance company will be declared ruin if the capital company value symbolized by 𝑈(𝑡) is negative. This research is expected can be a reference and help insurance field.