Title: Aspects of Valuation and Optimization in Life Insurance

Abstract: This thesis consists of five papers within the broad area of life insurance mathematics. There is no unifying topic, but many recurrent subtopics. In the first paper, we find an optimal hedging strategy for a portfolio of general life insurance contracts by using the criterion of local risk-minimization in a market with mortality derivatives. The second paper studies expected policyholder behavior in a multistate Markov chain model with deterministic intensities. Valuation techniques in the cases where policyholder behavior is modelled to occur independently or dependently of insurance risk, respectively, are discussed and studied numerically. The impact (quantitatively and computationally) of different simplifying assumptions are investigated for representative insurance contracts. In the third paper, we derive worst-case scenarios and reserves for an inhomogeneous portfolios of life insurance contracts in the case where the interest rate and the various transition intensities are mutually dependent. Numerical studies qualifying the standard formula of Solvency II are presented. In the fourth paper, we study the class of affine processes and obtain transform results which can be used for valuation of life insurance contracts modelled within general, hierarchical, multistate Markov chains where we allow for dependence between the interest rate and transition intensities. The fifth paper studies optimal surplus distribution strategies (by controlling either assets or liabilities) under different types of solvency constraints in a model with infinite time horizon where assets and liabilities are modelled by correlated, geometric Brownian motions.

Principal supervisor: Mogens Steffensen

Assessment committee:

Chairman: Prof. Jostein Paulsen, Math, Univerisity of Copenhagen

Prof. Stefan Weber, Leibniz Universität Hannover

Prof. Griselda Deelstra, Université Libre de Bruxelles