Multi-state Transition Models for Cash Flows

Abstract

As an extension of multiple decrement models, multi-state model of transitions is discussed in Chap. 5 when the transitions among the states are governed by Markov models. There are many instances in health insurance, disability income insurance, and vehicle insurance where the members move back and forth among states and may return to states they have previously left. For example, in disability income insurance, while modeling workers’ eligibility for various employee benefits, the states considered are (i) active, (ii) temporarily disabled, (iii) permanently disabled, and (iv) inactive which may include retirement, death, or withdrawal that can be defined as separate states. A Markov model is proposed to describe the probabilities of moving among these various states, including the possibility of moving back and forth between active and temporarily disabled states several times. In vehicle insurance in modeling insured automobile drivers’ ratings by the insurer, the states considered are (i) preferred, (ii) standard, and (iii) substandard. Thus, these states describe the insured’s driving record. The probabilities of transitions among these states can also be modeled by a Markov chain. Sometimes a state “gone” is considered to describe that the member is no longer insured. In health insurance, in long-term care, a commonly used model is continuing care retirement communities. In this model, residents may move among various states such as (i) independent living, (ii) temporarily in health center, (iii) permanently in health center, and (iv) gone. In insurance it is of interest to see the financial impact of these transitions. Multiple state models have proved to be appropriate models for an insurance policy in which the payment of benefits or premiums is dependent on being in a given state or moving between a given pair of states at a given time. Chapter 5 explores a Markov chain model to decide premium in continuing care retirement communities model in health insurance and a Markov process model for disability income insurance in employee benefit schemes. R code is provided for all the computations.