Insurance Ccompanies portfolio optimisation with possibilities of recovery after ruin

Abstract

This dissertation, is about a study on insurance companies that have experienced ruin but have a possibility of recovery from ruin. The study has proposed a perturbed mathematical model, analysed and used it for modelling the portfolio of insurance companies with possibilities of re covery after ruin. Return on investment and refinancing have been used as approaches for over coming ruin. The model was analysed for various cases of possibilities of recovery after ruin in the closed interval [0, 1]. The basic perturbed classical risk process was later compounded by refinancing and return on investment. The Hamilton-Jacobi-Bellman and Integro-Differential Equation of Volterra type were obtained. The Volterra Integro-Differential Equation for sur vival function of an insurance company was converted to a third order ordinary differential equation and later converted into a system of first order ordinary differential equations which was solved numerically using the fourth order Runge-Kutta method. The results indicate that the return on investment plays a vital role in reducing ultimate ruin and that as the possibility of recovery for insurance companies increases, the return on investment reduces ruin much faster. Also, the survival function increases with the increasing intensity of the counting pro cess but decreases with an increase in the instantaneous rate of stock return and return volatility. Because an insurance company faces more risks, these results also suggest that insurance com panies should increase their counting process since doing so will help the insurance companies in servicing more customers.