Investigating the Broken-Heart Effect: a Model for Short-Term Dependence between the Remaining Lifetimes of Joint Lives

We analyze the mortality of couples by fitting a multiple state model to a large insurance data set. We find evidence that mortality rates increase after the death of a partner and, in addition, that this phenomenon diminishes over time. This is popularly known as a “broken-heart” effect and we find that it affects widowers more than widows. Remaining lifetimes of joint lives therefore exhibit short-term dependence. We carry out numerical work involving the pricing and valuation of typical contingent assurance contracts and of a joint life and survivor annuity. If insurers ignore dependence, or mis-specify it as long-term dependence, then significant mis-pricing and inappropriate provisioning can result. Detailed numerical results are presented.

A Semi-Markov Multiple State Model for Reverse Mortgage Terminations

Reverse mortgages provide a mechanism for seniors to release the equity that has been built up in their home. At termination, the mortgagors are usually guaranteed to owe no more than the value of their property. The value of the reverse mortgage guarantee is heavily dependent on the maturity or termination date, which is uncertain. In this paper, we model reverse mortgage terminations using a semi-Markov multiple state model which incorporates three different modes of exit: death, entrance into a long-term care facility, and voluntary prepayment. We apply the proposed model specifically to develop the valuation formulas for roll-up mortgages in the UK and Home Equity Conversion Mortgages (HECMs) in the USA. We examine the significance of each mode of termination by valuing the contracts allowing progressively for each mode. On the basis of our model and assumptions, we find that both health related terminations and voluntary (non-health related) terminations significantly impact the contract value. In addition we analyze the premium structure for US reverse mortgage insurance, and demonstrate that premiums appear to be too high for some borrowers, and substantial cross-subsidies may result.

Some Notes on the Average Duration of an Income Protection Claim

Cordeiro (2002a) has presented a multiple state model for Income Protection (formerly known as Permanent Health Insurance) which enables us to analyse claims by cause of disability. In that paper average claim durations conditioned on recovery have been calculated. Since, when an Income Protection claim is reported, the insurance company never knows whether it will end in recovery, in death or in expiry, to analyse only average claim durations conditioned on recovery could be misleading, specially for the people responsible for the claims control process. The main purpose of this paper is to calculate average claim durations conditioned on death and average claim durations not conditioned on any particular mode of claim termination. We calculate these claim durations for different deferred periods, causes of disability and ages at the beginning of sickness and we analyse the results obtained.

Some Notes on the Average Duration of an Income Protection Claim

Cordeiro (2002a) has presented a multiple state model for Income Protection (formerly known as Permanent Health Insurance) which enables us to analyse claims by cause of disability. In that paper average claim durations conditioned on recovery have been calculated.Since, when an Income Protection claim is reported, the insurance company never knows whether it will end in recovery, in death or in expiry, to analyse only average claim durations conditioned on recovery could be misleading, specially for the people responsible for the claims control process.The main purpose of this paper is to calculate average claim durations conditioned on death and average claim durations not conditioned on any particular mode of claim termination. We calculate these claim durations for different deferred periods, causes of disability and ages at the beginning of sickness and we analyse the results obtained.

Measuring Process Risk in Income Protection Insurance

The main objective of this paper is to measure the process error for a portfolio of independent disability insurance policies in a multiple state modelling context. We consider the calculation of premiums for a portfolio of income protection insurance policies in a stochastic environment represented both by random transitions in the underlying multiple state model and random external economic factors in the form of stochastic investment returns and inflation. We also investigate the sensitivity of the process error to the level of volatility incorporated in a given model using suitably defined risk measures. We then draw conclusions and identify possible avenues for future research.

Measuring Process Risk in Income Protection Insurance

The main objective of this paper is to measure the process error for a portfolio of independent disability insurance policies in a multiple state modelling context. We consider the calculation of premiums for a portfolio of income protection insurance policies in a stochastic environment represented both by random transitions in the underlying multiple state model and random external economic factors in the form of stochastic investment returns and inflation. We also investigate the sensitivity of the process error to the level of volatility incorporated in a given model using suitably defined risk measures. We then draw conclusions and identify possible avenues for future research.