Approximations of ruin probabilities under financial constraints.

Abstract

This thesis studies the approximate ruin probabilities under financial constraints which in- clude the rate of inflation, constant interest rate, and taxation. When the surplus falls below zero, the insurance company is technically considered ruined. The main objective of the study included; to establish a risk model which takes into account all the financial con- straints,to establish analytically, the formula for the approximation of ruin probabilities for both exponentially and sub-exponentially distributed claims, to compare the approximate ruin probabilities from our model and those of the classical Cram´er-Lundberg model, and finally to compare the convergence of Pareto and Log-normal distributions for the formu- lated model. An extensive review of literature is done and much attention is given to the research by Albrecher and Hipp whose research successfully formulates Lundberg’s (classi- cal) risk process in presence of tax. A risk model is formulated in the present study whose premium inflow is influenced by inflation and a constant interest rate. We thereafter in- voke the Albrecher and Hipp loss-carried-forward tax scheme from which an approximation of probability of ruin for the light tailed (exponential) distribution is derived for an exact solution. Then, a suitable formula for the claims with sub-exponential distribution is also derived using the Pollaczek-Khintchine formula. Simulations are hence done using R and Microsoft Excel in this regard. The results show that approximating ruin probability when taking into account all the three financial constraints gives desirable results as compared to those of classical Lundberg model. The comparison between the two heavy-tailed distribu- tions under the concept of limiting density ratio, shows that a Log-normal density exhibit a lighter tail, thus converges faster. However, the model is open for further improvements, specifically to incorporate a stochastic rates of interest. The results of this study will hence guide the policymakers and the insurance industry to make informed decisions to help guard against future ruin as witnessed in local insurance companies in Kenya and globally.