A Note on Stochastic Survival Probabilities and Their Calibration

ICER Applied Mathematics Working Paper No. 1 - 2005

18 Pages Posted: 9 May 2005

See all articles by Elisa Luciano

Elisa Luciano

Collegio Carlo Alberto; University of Turin - Department of Statistics and Applied Mathematics

Elena Vigna

University of Turin - Faculty of Economics; Collegio Carlo Alberto; CeRP

Date Written: January 2005

Abstract

In this note we use doubly stochastic processes (or Cox processes) in order to model the evolution of the stochastic force of mortality of an individual aged x. These processes have been widely used in the credit risk literature in modelling the default arrival, and in this context have proved to be quite flexible and useful. We investigate the applicability of these processes in describing the individual's mortality, and provide a calibration to the Italian case. Results from the calibration are twofold. Firstly, the stochastic intensities seem to better capture the development of medicine and long term care which is under our daily observation. Secondly, when pricing insurance products such as life annuities, we observe a remarkable premium increase, although the expected residual lifetime is essentially unchanged.

JEL Classification: G22, J11

Suggested Citation

Luciano, Elisa and Vigna, Elena, A Note on Stochastic Survival Probabilities and Their Calibration (January 2005). ICER Applied Mathematics Working Paper No. 1 - 2005, Available at SSRN: https://ssrn.com/abstract=711704 or http://dx.doi.org/10.2139/ssrn.711704

Elisa Luciano (Contact Author)

Collegio Carlo Alberto ( email )

via Real Collegio 30
Moncalieri, Torino 10024
Italy

HOME PAGE: http://www.carloalberto.org/people/faculty/fellows/luciano/

University of Turin - Department of Statistics and Applied Mathematics ( email )

Corso Unione Sovietica 218 bis
Turin, I-10122
Italy
+ 39 011 6705230 (Phone)

Elena Vigna

University of Turin - Faculty of Economics ( email )

Dipartimento di Statistica e Matematica Applicata
Corso Unione Sovietica 218 bis
Torino, 10134
Italy

Collegio Carlo Alberto ( email )

via Real Collegio 30
Moncalieri, Torino 10024
Italy

CeRP ( email )

Via Real Collegio, 30
Moncalieri, Turin 10024
Italy

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