PhD defence by Philipp Carsten Hornung

Forward and backward methods in life insurance: Theoretical advances and applications

PhD defence by Philipp Carsten Hornung

Assessment Committee

Associate Professor Jesper Lund Pedersen, Department of Mathematical Sciences, University of Copenhagen (Chairperson)
Professor Julia Eisenberg, Technische Universität Wien
Professor Marcus Christian Christiansen, Universität Oldenburg

Supervisors

Professor Mogens Steffensen
Associate Professor Christian Furrer

Department

Department of Mathematical Sciences

Place

Building: HCØ, Room: Aud. 5, Universitetsparken 5, 2100 København

Email address to gain access to the thesis: pcho@math.ku.dk.
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Short description of the thesis

This thesis contains a series of investigations related to the use of forward and backward methods for the valuation and design of multi-state life insurance contracts. First, we study the valuation of insurance contracts with collective effects using a mean-field approximation and prove that, for large cohorts, the value of an insurance contract converges towards its mean-field counterpart. We then introduce collective health claims to the classic semi-Markov disability model and illustrate the efficiency of the mean-field approximation in a practice-oriented numerical example. Second, we prove a novel existence and uniqueness result for the worst- and best-case reserves of contracts with reserve-dependent payments and solve a robust consumption-insurance problem with power utility preferences. Finally, we discuss the preferences for a smooth consumption rate in terms of the components (initial value, drift, volatility) of the consumption rate both qualitatively and quantitatively.