Effects of Dependent Claims on The Probability of Ruins, The Time to Ruin Given Ruin Occurs

ABSTRACT 

Ruin basically occurs to an insurance company when the claims paid out supersedes its initial capital and total premiums accumulated. In the classical theory of risk, the surplus is a significant model that deals with how long an insurance company's capital or surplus evolves. The first time ruin occurs is very crucial and the business must try to prevent it from happening again because it makes the business inefficient and inoperable. The time to ruin is so much a function of the initial capital and the way in which the insurance company's business books are priced. An insurance company has no control over how claims are issued, can attempt and handle its excess to assess the number of claims that will arise over time. The hypothesis that individual claims occur separately is one of the assumptions of the excess method. But this premise of independence is no longer true and sensible, as individual risks are generally homogeneous and share comparable features that claims from one eventuality could cause claims from another. In this thesis, the impacts of dependent claims on the likelihood of ruin and the time-to-ruin was examined also proposed premium adjustment when there is claim dependence. the objectives of this study is to determine how dependent claims, affect the likelihood of ruin and time to ruin of insurance companies in Ghana. And also to determine the time left for an insurance company to go to ruin when the assumption of dependency claims hold. The study employed Pollaczek-Khinchine formula, which was used to estimate probability of ruin and time to ruin, copulas and Pearson correlation was used to determine claims dependence. The study found out that the moment of ruin occurs more quickly in the presence of dependent claims. Therefore, the study recommended an adjustement of premims to hedge against negative cash flows in the assumption of claims dependent.