Grant: Discovery Grants Program - Individual

This application proposes work with both theoretical and applied aspects. On the theoretical side, this proposal is related to two variants of risk models, which are described in the following. (1) Risk processes with discounted claims. In insurance practice, there usually is a time delay between the collection of the premiums and the payment of claims. In some lines of business, the delay could be as long as twenty years. Therefore, it is important to consider the time value of money in risk process by discounting the claims. Moments and related ruin problems for classical risk processes with discounted claims has been studied extensively in the literature. However, there are not many theoretical results for ruin problems in the Sparre-Andersen risk models with discounted claims. Therefore, this topic will form one of the primary research subjects of this proposal.(2) Perturbed risk processes with barriers. Ruin probabilities for perturbed risk processes have been studied extensively in the risk theory literature. However, it seems that not much work has appeared relating to the perturbed risk model with barriers, where it is assumed that when the surplus exceeds the barrier, dividends are paid to the stakeholders. Therefore, in this project, I intend to study such properties of the risk processes under a barrier strategy. Quantities of interests include the distribution and the moments of the discounted expected dividends and the expected penalty at ruin.On the application side, this proposal describes a collaborative project entailing techniques in actuarial science and in engineering sciences to evaluate earthquake insurance.