Princing insurance policies in Rwanda using multi-state markov chain models: Case study for Sanlam

Abstract

This thesis seeks to apply a model for pricing insurance policies. Some insurance companies are facing increasing financial losses because of large claims, which are not equivalent to the premiums. Continuous-time Markov chain has been used to price insurance policies, at the beginning elementary theory of continuous-time Markov chain is introduced and some basic properties of Markov chain, transition proba bilities, force of intensity. Next part of thesis, the reader is introduced to some application of Kolmogorov differential equation for a multi-state model as they are widely used in actuarial science because they provide a convenient way for represent ing changes in people’s status. The multi-state models have been assumed to satisfy the Markov properties. The continuous-time Markov chain have been used in calcu lating the transition intensities and transition probabilities have been calculated using Kolmogorov differential equation. Transition intensities, transition probabilities are used to calculate the expected present values of benefit, the annuities of death ben efit and the premiums as applied to insurance products for Sanlam. Results reveal that the premiums and the benefits of transition between disability state to death are highest compared to the others. The conclusion is increasing premiums leads to more benefits which is in line with real reality