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Kuslan Kuslan
Risk Management Group, LIPPO Bank, Indonesia
Mathematics

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On Estimating the Transition Probabilities: A Case Study Sutawanir Darwis; Kuslan Kuslan
Jurnal Matematika & Sains Vol 13, No 1 (2008)
Publisher : Institut Teknologi Bandung

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Abstract

In actuarial science, a multistate process deals with the joint distribution of two random variables: time until termination and cause of the termination. In a three state process (active, retired, death), an insured in active state canbecome retired according to a force of decrement of retired, insured in retired state can move to death state accordingto a force of decrement of mortality. The main issues are the development of the estimation methods for transitionprobabilities and its implementation on a real data set. Analytical studies of multistate model are well developed in theliterature. However, the empirical studies based on real data set rarely reported. Furthermore, published works focusedon modeling the transition probabilities as function of period of transition. This work presents an extension of transitionprobabilities as function of age of insured and period of transition. A case study of modeling three state process andmethodology for estimating the model parameters from an insurance database under constant forces of decrement ispresented. The forces of decrement was estimated using single decrement moment estimation procedure, and yields atransition probability for a three state models. This paper aims to contribute to the development of empirical transitionprobabilities of multistate model based on real data set as an alternative to the traditional approach to doubledecrement modelling.
Spectral Decomposition of Transition Matrix Sutawanir Darwis; Kuslan Kuslan
Jurnal Matematika & Sains Vol 13, No 3 (2008)
Publisher : Institut Teknologi Bandung

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Abstract

The transition probabilities of a two-state Markov process can be determined explicitly. The modeling of forcetransition of two state Markov process using double decrement approach is well developed in the literature. However,the approaches are mainly analytic or illustrative and are based on small data set. The study based on large data set arerarely published. For higher number of states, the computation of transition probabilities is laborious, and analternative method is needed. This work aims to propose a spectral approach of forces of transition that attempts toaddress the issues. The method is based on results that are available when a Markov process with constant forces oftransition is assumed. In this case, transition probabilities are obtained regardless of the number of states. A differentialequation is used to express the relationship between forces of decrements and transition probabilities, and by assumingconstant force, the explicit solution is reduced to spectral decomposition of force of decrements. The results are thevisualization of transition probabilities, and a contribution for the development of double decrement table. The maincontributions of this work are a spectral representation of transition probabilities and a multistate approach to doubledecrement modeling.
Co-Authors Sutawanir Darwis