PhD Defense by Jamaal Ahmad

Matrix methods in multi-state life insurance

This thesis considers matrix methods in multi-state life insurance, with an emphasis on techniques related to inhomogeneous phase-type distributions (IPH) and product integrals. We start out with developing an expectation-maximization (EM) algorithm for statistical estimation of general IPHs. Then we introduce a new class of multi-state models, the so-called aggregate Markov model, which allows for non-Markovian modeling with most of the analytical tractability of Markov chains preserved. Using techniques related to IPHs, we derive distributional properties, computational schemes for life insurance valuations with duration-dependent payments, and statistical estimation procedures based on the EM algorithm for general IPHs. Special attention is given to a case with a reset property, where the aggregate Markov model is semi-Markovian. We then move on and consider Markov chain interest rate models and show that bond prices are survival functions of IPHs. This allows for calibration via EM algorithms for phase-type distributions. Then we consider a multivariate payment process and derive higher order moments of its present value. Finally, we consider computation of market values of bonus payments in multi-state with-profit life insurance, where numerical procedures based on simulation of financial scenarios and classic analytical methods for insurance risk are developed.

Thesis for download: Matrix methods in multi-state life insurance

Supervisor: Professor Mogens Bladt, University of Copenhagen
Co-supervisor: Professor Mogens Steffensen, University of Copenhagen

Assessment committee:
Professor Thomas Mikosch (chairperson), University of Copenhagen
Professor Hansjörg Albrecher, University of Lausanne, Switzerland
Professor Emeritus Søren Asmussen, Aarhus University, Denmark