On Estimating the Transition Probabilities: A Case Study
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 can become
retired according to a force of decrement of retired, insured in retired state
can move to death state according to a force of decrement of mortality. The main issues are the development of the estimation methods for transition probabilities
and its implementation on a real data set. Analytical studies of multistate
model are well developed in the literature. However, the empirical studies
based on real data set rarely reported. Furthermore, published works focused on modeling the transition
probabilities as function of period of transition. This work presents an
extension of transition probabilities as function of age of insured and period
of transition. A case study of modeling three state process and methodology for
estimating the model parameters from an insurance database under constant
forces of decrement is presented. The forces of decrement was estimated using
single decrement moment estimation procedure, and yields a transition
probability for a three state models. This paper aims to contribute to the
development of empirical transition probabilities of multistate model based on
real data set as an alternative to the traditional approach to double decrement
modelling.
Author: Sutawanir Darwis, and
Kuslan
Kode Jurnal: jpmatematikagg080002
