Forward mortality and other vital rates - are they the way forward? (English) Zbl 1231.91459

Norberg, Ragnar

Insur. Math. Econ. 47, No. 2, 105-112 (2010).

Summary: We present a comparative study of stochastic interest and stochastic mortality showing that, despite a virtual similarity, the two concepts are fundamentally different. The notion of forward mortality rate, fetched from finance and now the latest thing in actuarial science, is predicted to soon go out of fashion. Trying it on, it does not fill the measurements of a well-made theoretical concept: there is an element of arbitrariness in its very definition, it disobeys certain self-evident parity requirements, and it fails to generalize to more complex models. It is concluded that forward rate modeling, while passable in the context of interest, is not the way forward in the context of mortality and more general life history analysis.

MSC:

91G30	Interest rates, asset pricing, etc. (stochastic models)
60G35	Signal detection and filtering (aspects of stochastic processes)
62N05	Reliability and life testing
91B30	Risk theory, insurance (MSC2010)

Keywords:

stochastic interest; stochastic mortality; credit risk; rates vs. intensities; multi-state life insurance models

References:

[1]	Andersen, P.K.; Borgan, Ø.; Gill, R.D.; Keiding, N., Statistical models based on counting processes, (1993), Springer-Verlag · Zbl 0769.62061
[2]	Björk, T., Arbitrage theory in continuous time, (2004), Oxford University Press · Zbl 1140.91038
[3]	Cairns, A.J.G.; Blake, D.; Dowd, K., Pricing death: frameworks for the valuation and securitization of mortality risk, ASTIN bulletin, 36, 79-120, (2006), First as working paper from Heriot-Watt University, 2004 · Zbl 1162.91403
[4]	Dahl, M., Stochastic mortality in life insurance: market reserves and mortality- linked insurance contracts, Insurance: mathematics & economics, 35, 113-136, (2004) · Zbl 1075.62095
[5]	Dahl, M.; Møller, T., Valuation and hedging of life insurance liabilities with systematic mortality risk, Insurance: mathematics & economics, 39, 193-217, (2006) · Zbl 1201.91089
[6]	Milevsky, M.; Promislow, D., Mortality derivatives and the option to annuitise, Insurance: mathematics & economics, 29, 3, 299-318, (2001) · Zbl 1074.62530
[7]	Miltersen, K.R., Persson, S.-A., (2005). Is mortality dead? Stochastic forward force of mortality rate determined by no arbitrage, Working paper, Norwegian School of Economics and Business administration. Online version available at http://www.mathematik.uni-ulm.de/carfi/vortraege/downloads/DeadMort.pdf.