Aggregated Markov Models in Life Insurance

Specialeforsvar: Nikolaj Vinkel

Titel: Aggregated Markov Models in Life Insurance: An efficient approach to valuation in path dependent multi-state

Abstract: As a consequence of Solvency II, methods for market consistent valuation of life insurance liabilities have become increasingly more important in actuarial practice and academia. For valuation of disability related products, especially disability annuities, this has led to an increased interest in the practical properties of path dependent multi-state models and specifically the time-inhomogeneous semi-Markov model, which can properly catch the duration effects in a disability course of an insured. In this thesis, we examine the practical properties of the currently available valuation methods in the semi-Markov model, which are very computationally demanding compared to the classic path independent Markov model. This inspires the introduction of the so-called aggregated Markov model, which is a multistate model that allows for path dependency while retaining the computational properties of the Markov model. In particular, we present a subset of the aggregated Markov model with a reset property, which fits into the semi-Markov framework. This special case with the reset property and the extent to which it can emulate a general semi-Markov model is the main focus of this thesis as we present an approximation scheme for a general semi-Markov model within this setup. The approximation method presented is inspired by the so-called Erlangization method, which is used to approximate deterministic jump times in a timecontinuous jump process. The Erlangization method is in addition used to approximate the time of a waiting period, which is often a part of a disability annuity contract in practice
that stipulates that the payments are only disbursed after the waiting period is over. This then allows for cash flow calculations with duration independent payments, which turns out to be significantly simpler in the aggregated Markov model. The main result of this thesis is then a practical examination of the computational load and precision we can obtain using the classic methods for valuation in a semi-Markov model for a disability annuity with a waiting period compared to the presented approximation scheme of the semi-Markov model and the waiting period of the payments in conjunction. It is demonstrated here that we are able to obtain precise approximations in a computationally efficient manner with the presented approximation scheme.

Vejledere: Mogens Bladt, Jamaal Ahmad
Censor:     Kristian Buchardt, PFA