Insurance risk analysis with dependence and reinsurance

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Classical risk theory usually studies a reserve process for a company or a line of business. However, a company could run several lines of business or have several subcompanies. The reserve processes of these lines of business form a multivariate dependent risk process. Even for different companies, the reserve processes could be correlated due to some common economic and financial factors. Furthermore, when an insurance company has a reinsurance treaty with a reinsurance company, the reserve risk processes of the two companies are correlated as well. Thus, dependence naturally appears in a multivariate reserve risk process and in the study of reinsurance. In this project, we will focus on two-dimensional reserve risk processes. For each line of business in a two-dimensional reserve risk model, we define default time as the first time when the reserve of the line falls below a certain level. We will study the probabilities of different types of defaults. We will also study the expected total discounted expenses related to claims of each line of business up to default times. Such expected total discounted expenses can be used to study many default-related quantities and to determine the capital requirements for each line of business. We assume that a reinsurance strategy is applied to one line of business. We will study the optimal reinsurance strategies for dependent lines of business under different optimization criteria. Further, we will consider economic and financial factors, such as interest rates and dividends, in two-dimensional reserve risk processes and discuss the influence of economic and financial factors on default probabilities. The project will provide new stochastic models for insurance risk analysis with dependence and reinsurance, and reveal the impact of dependence, reinsurance, and some economic and financial factors on default times and default probabilities. The anticipated results will be useful not only in insurance risk analysis but also in credit risk analysis and other fields of applied probability.