Modelling, Quantifying and Managing Risk in Insurance and Related Areas

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Insurance is a risk-taking business, which makes modelling, quantifying, and managing risk crucial to the success of any insurance organization. Advances in computing technology and the maturing of quantitative methods have meant a significant increase in the use of quantitative models in actuarial science. My proposed research will address insurance risk problems in several areas of general insurance, such as stochastic claim reserving, pricing, and insurance risk theory. The models and methods I propose will be explored in operational risk and related areas. In stochastic claim reserving, I will explore ways to predict the Reported But Not Settled (RBNS) reserve and the Incurred But Not Reported (IBNR) reserve that occur in Property and Casualty Insurance - among the most important components of an insurance company's balance sheet. In particular, I plan to investigate the use of marked Cox processes and their generalizations. The use of mixture of experts distributions under various Hidden Markov Model assumptions will be at the core of our reserving or credibility type techniques. I will develop Expectation Maximization type algorithms for fitting the model parameters that will possibly allow for the inclusion of covariate information. The dependence structures among reporting delays, settlement delays, and claim sizes will be considered in detail via parametric and non-parametric distributions, copulas, and partially specified joint distributions. A second stage of the research will be based on work in insurance risk theory. With my team, I will focus on the assessment of global risk associated with the insurance business in an attempt to evaluate solvency requirements. To this end, I will replace the classical Poisson, renewal, and Markovian type risk models with more realistic and sophisticated ones. My new models will be able to consider more general point processes that can account for reporting and settlement delays and for multiple payments associated with the accident events. I will mainly focus on multivariate risk models that consider various dependence structures introduced via frequencies, severities, and capital infusions. The quantification and management of risk will be determined via ruin related measures that will account potentially for reserves for those events that are not reported or not settled prior to the valuation time. I expect my research results to have a substantial long-term impact on the insurance industry. I anticipate that the models, methodologies, and numerical procedures developed in this proposal will especially interest actuaries, as the projects I am working on come from the insurance industry. Moreover, these methods will be adapted and applied to other areas such as managing operational risk.