Abstract
This study examines the impact of losses and defaults using ruin theory and uses a heterogeneous portfolio of loans extending specifically to banking institutions. Simply put, this study focuses on the time at which default occurs in order to assist banks to detect defaults before they occur. This is done through the Sparre Anderson Model and the associated ruin probabilities linked to the stochastic flows of heterogeneous loans. The dissertation derives the Cramér-Lundberg-type bounds for ruin probability (through the Sparre Anderson Model) while also determining the impact of changing the interest rate, time to maturity and probability of default of different loan sizes. In addition, the Cramér-Lundberg-type bounds are derived to determine the lower and upper ruin probability bounds. The time of ruin is analysed through the Laplace Transform. The results show that if the adjustment coefficient declines, the ruin probability will increase, resulting in an increase in the probability of default. The values of 𝐶− and 𝐶+ (the upper and lower bound, respectively) are meaningful in deriving the bounds for ruin probability. This dissertation finds that obtaining the value of the adjustment coefficient makes it possible to determine the constants of the bounds which are a risk measure for the default exposure of loans. Increasing the premium increases the probability of default. This means that financial institutions should apply caution when increasing their premiums.
M.Com. (Financial Economics)