Abstract
M.Com. (Financial Economics)
Ruin theory is a predominant topic in actuarial science and many researchers have brought their contributions in it to make the theory close to reality. Historically, the pioneers of ruin theory have assumed a risk model that is not affected by the force of interest. However, it is well-known that insurance companies operate in an economic environment where the force of interest plays an important role, hence the study of ruin probability without considering the force of interest is flawed in reality.
In this thesis, we consider Ramsay’s model, modified by the inclusion of random interest rate on the surplus process, where we investigate the effect of random interest rate on the ruin probability. Autoregressive model is introduced to model the randomness of the interest rate. Based on the statistics’ test, we found that The Three- Months South Africa Treasury Bill Rates (TBR) used in this study can be modelled by an autoregressive structure of order one. We then derive exponential type upper bounds for the ruin probability by using a renewal recursive technique. Finally, we provide numerical examples where the length of the sickness period and that of the healthy period follow an Erlang distribution to illustrate our results. We found that the probability of ruin is very small when we considered a random interest rate in the Ramsay’s risk model unlike the results obtained by Adekambi (2013) when he considered a constant interest rate in the Ramsay model.