Matrix methods in multi-state life insurance

Research output: Book/ReportPh.D. thesisResearch

This thesis considers matrix methods in multi-state life insurance, with an emphasis on techniques related to inhomogeneous phase-type distributions (IPH) andproduct integrals. We start out with developing an expectation-maximization (EM)algorithm for statistical estimation of general IPHs. Then we introduce a newclass of multi-state models, the so-called aggregate Markov model, which allowsfor non-Markovian modeling with most of the analytical tractability of Markovchains preserved. Using techniques related to IPHs, we derive distributional properties, computational schemes for life insurance valuations with duration-dependentpayments, and statistical estimation procedures based on the EM algorithm forgeneral IPHs. Special attention is given to a case with a reset property, wherethe aggregate Markov model is semi-Markovian. We then move on and considerMarkov chain interest rate models and show that bond prices are survival functionsof IPHs. This allows for calibration via EM algorithms for phase-type distributions.Then we consider a multivariate payment process and derive higher order momentsof its present value. Finally, we consider computation of market values of bonuspayments in multi-state with-profit life insurance, where numerical procedures basedon simulation of financial scenarios and classic analytical methods for insurancerisk are developed.
Original languageEnglish
PublisherDepartment of Mathematical Sciences, Faculty of Science, University of Copenhagen
Publication statusPublished - 2023

ID: 347694298