Jingyu (Jayla) Chen - MSc Defence

Title: The Discounted Penalty Function and the Distribution of The Total Dividend Payments in a Multi-threshold Markovian Risk Model


In this thesis, we study the discounted penalty function and the total dividend payments in a risk model with a multi-threshold dividend strategy, where the claim arrivals are modeled by a Markovian arrival process (MAP) and the claim sizes are correlated with the inter-claim times. Systems of integro-differential equations in matrix forms are derived for the discounted penalty function and the moments of the total dividend payments prior to ruin. A recursive approach based on the integro-differential equations is then provided to obtain the analytical solutions. In addition to the differential approach, by employing some new obtained results in the actuarial literature, another recursive approach with respect to the number of layers is also developed for the expected discounted dividend payments to increase the computational feasibility. Examples with exponentially distributed claim amounts are illustrated numerically.