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Non mean reverting affine processes for stochastic mortality

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Elisa Luciano ()
Elena Vigna ()

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Abstract

In this paper we use doubly stochastic processes (or Cox processes) in order to model the random evolution of mortality of an individual. These processes have been widely used in the credit risk literature in modelling default arrival, and in this context have proved to be quite flexible, especially when the intensity process is of the affine class. We investigate the applicability of affine processes in describing the individual's intensity of mortality, and provide a calibration to the Italian and UK populations. Results from the calibration seem to suggest that, in spite of their popularity in the financial context, mean reverting processes are not suitable for describing the death intensity of individuals. On the contrary, affine processes whose deterministic part increases exponentially seem to be appropriate. As for the stochastic part, negative jumps seem to do a better job than diffusive components. Stress analysis and analytical results indicate that increasing the randomness of the intensity process results in improvements in survivorship.

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Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 4-2005.

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Length: 29 pages
Date of creation: Mar 2005
Date of revision:
Handle: RePEc:icr:wpmath:4-2005

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Related research
Keywords: doubly stochastic processes (Cox processes); stochastic mortality; affine processes;

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Find related papers by JEL classification:
G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies
J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends and Forecasts

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  13. Larry G. Epstein & Massimo Marinacci, 2006. "Mutual Absolute Continuity of Multiple Priors," Carlo Alberto Notebooks 19, Collegio Carlo Alberto. [Downloadable!]
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  14. Giovanni Mastrobuoni, 2006. "The Social Security Earnings Test Removal: Money Saved or Money Spent by the Trust Fund?," Working Papers 892, Princeton University, Department of Economics, Industrial Relations Section.. [Downloadable!]
  15. Elisa Luciano & Wim Schoutens, 2006. "A Multivariate Jump-Driven Financial Asset Model," Carlo Alberto Notebooks 29, Collegio Carlo Alberto. [Downloadable!]
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  16. Elisa Luciano & Elena Vigna, 2005. "Non mean reverting affine processes for stochastic mortality," ICER Working Papers - Applied Mathematics Series 4-2005, ICER - International Centre for Economic Research. [Downloadable!]
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  17. Daniela Del Boca & Robert M. Sauer, 2006. "Life Cycle Employment and Fertility Across Institutional Environments," IZA Discussion Papers 2285, Institute for the Study of Labor (IZA). [Downloadable!]
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  26. Matteo Triossi, 2006. "Application Costs in Sequential Admission Mechanisms," Carlo Alberto Notebooks 23, Collegio Carlo Alberto. [Downloadable!]
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  29. Giovanni Mastrobuoni & Wioletta Dziuda, 2005. "The Euro Changeover and its Effects on Price Transparency and Inflation," Carlo Alberto Notebooks 26, Collegio Carlo Alberto, revised 2006. [Downloadable!]
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  30. Daniela Del Boca & Christopher J. Flinn, 2005. "Household Time Allocation and Models of Behavior: A Theory of Sorts," Carlo Alberto Notebooks 8, Collegio Carlo Alberto, revised 2006. [Downloadable!]
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  31. Londregan, John & Vindigni, Andrea, 2006. "Voting as a Credible Threat," Papers 10-04-2006, Princeton University, Research Program in Political Economy. [Downloadable!]
  32. Andrea Buffa & Giovanna Nicodano, 2006. "Should Insider Trading be Prohibited when Share Repurchases are Allowed?," Carlo Alberto Notebooks 16, Collegio Carlo Alberto. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Complete Monotone Quasiconcave Duality," Carlo Alberto Notebooks 80, Collegio Carlo Alberto. [Downloadable!]
  2. Elena Vigna, 2009. "Mean-variance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes," Carlo Alberto Notebooks 108, Collegio Carlo Alberto, revised 2009. [Downloadable!]
  3. Esteban Jaimovich, 2008. "Adverse Selection and Entrepreneurship in a Model of Development," Carlo Alberto Notebooks 78, Collegio Carlo Alberto. [Downloadable!]
  4. Daron Acemoglu & Davide Ticchi & Andrea Vindigni, 2008. "A Theory of Military Dictatorships," Carlo Alberto Notebooks 74, Collegio Carlo Alberto. [Downloadable!]
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  5. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2007. "Learning and Disagreement in an Uncertain World," Carlo Alberto Notebooks 48, Collegio Carlo Alberto. [Downloadable!]
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  6. Ales Cerný & Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2008. "On the Computation of Optimal Monotone Mean-Variance Portfolios via Truncated Quadratic Utility," Carlo Alberto Notebooks 79, Collegio Carlo Alberto. [Downloadable!]
  7. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2008. "Objective and Subjective Rationality in a Multiple Prior Model," Carlo Alberto Notebooks 73, Collegio Carlo Alberto, revised 2008. [Downloadable!]
  8. Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2006. "A note on stochastic survival probabilities and their calibration," ICER Working Papers - Applied Mathematics Series 5-2006, ICER - International Centre for Economic Research. [Downloadable!]
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  9. Alexander Melnikov & Yuliya Romanyuk, 2006. "Efficient Hedging and Pricing of Equity-Linked Life Insurance Contracts on Several Risky Assets," Working Papers 06-43, Bank of Canada. [Downloadable!]
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  10. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci, 2007. "Revealed Ambiguity and Its Consequences: Updating," Carlo Alberto Notebooks 44, Collegio Carlo Alberto. [Downloadable!]
  11. Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2007. "Modelling stochastic mortality for dependent lives," Carlo Alberto Notebooks 43, Collegio Carlo Alberto. [Downloadable!]
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  12. Elisa Luciano & Elena Vigna, 2006. "Non mean reverting affne processes for stochastic mortality," Carlo Alberto Notebooks 30, Collegio Carlo Alberto. [Downloadable!]
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  13. Russell Gerrard & Bjarne Højgaard & Elena Vigna, 2008. "Choosing the Optimal Annuitization Time Post Retirement," Carlo Alberto Notebooks 76, Collegio Carlo Alberto. [Downloadable!]
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