New directions in insurance loss modeling, ruin theory and their applications

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This research project continues the search for new theoretical and practical results in mathematical risk theory, connecting the area with other insurance or financial areas, such as insurance loss modeling, claim reserving and operational risk management. Realistic scenarios are considered when two or more insurance companies are at play at the same time. Situations where a reinsurer covers parts of the insurer losses, or where two or more insurers try to determine an optimal risk-sharing strategy that minimizes certain risks measures, will be pursued in details. The incurred but not reported loss reserve, and the reported but not settled reserve are important quantities in claim reserving, and will be included in the analysis of the surplus of an insurance company via its classical ruin related measures - the time to ruin, the surplus prior to ruin and the deficit at ruin.On a more practical side, modeling insurance losses is one of the most challenging problems for actuaries. An important question to be addressed in this proposal is the identification of potential candidates which can be used for fitting loss amounts when dealing with truncated and censored data sets. Due to its very appealing properties (denseness, closure etc.), the mixed Erlang class of distributions will play the main role in developing several fitting algorithms based on the well-known EM method. Potential applications of the proposed Erlang based methods in claim reserving will be studied in detail. Financial institutions are exposed to a variety of risks such as, strategy risk, reputation risk, market risk, credit risk, business risk, operational risk, liquid risk, and so on. Among these risks, market, credit and operational risks can be easily quantified in practice. In this project we are interested in measuring the operational risk according to the Advanced Measurement Approach (AMA) proposed in the Basel II directive. In order to avoid simulation, we are interested in finding closed form analytic solutions for the distribution of the overall losses associated to the operational risk, taking into consideration certain dependence structures that may occur among the different units of measurement.