On the forward rate concept in multi-state life insurance

Similarly to the notion of modeling credit risk by using forward credit default spread rates, mortality risk in life insurance contracts is nowadays often modeled by using forward mortality (spread) rates. More recently, this concept has also been discussed for more complex life insurances that incl...

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Bibliographic Details
Published in:Finance and stochastics 2015-04, Vol.19 (2), p.295-327
Main Authors: Christiansen, Marcus C., Niemeyer, Andreas
Format: Article
Language:English
Subjects:
Actuarial assumptions
Demography
Derivatives
Disability insurance
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Health inequality
Insurance
Insurance policies
Interest rates
Life insurance
Management
Mathematics
Mathematics and Statistics
Mortality
Multivariate analysis
Probability Theory and Stochastic Processes
Quantitative Finance
Securitization
Solvency
Statistics for Business
Stochastic models
Stochastic processes
Studies
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Summary:Similarly to the notion of modeling credit risk by using forward credit default spread rates, mortality risk in life insurance contracts is nowadays often modeled by using forward mortality (spread) rates. More recently, this concept has also been discussed for more complex life insurances that include multiple lives or intermediate states that correspond to the health status of the insured. For consistency purposes and for technical reasons, most authors assume that the underlying financial and demographic events are stochastically independent. In the present paper, we study sufficient and necessary conditions under which general transition forward rates are indeed consistent with respect to the relevant insurance claims. This shows the theoretical limitations of the forward rate concept in life insurance. Our study is based on a model where the underlying financial and demographical developments are diffusion processes driven by a multivariate Brownian motion. This allows us to investigate independence properties by analyzing the asymptotic behavior of mixed (conditional) moments. In particular, we obtain that for joint life and disability insurance policies, some specific demographic events need to be dependent in order to ensure consistency.
ISSN:0949-2984
1432-1122
DOI:10.1007/s00780-014-0244-9