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Continuous affine processes: transformations, Markov chains and life insurance

Published online by Cambridge University Press:  10 June 2016

Kristian Buchardt
Affiliation:
University of Copenhagen and PFA Pension
Corresponding
E-mail address:

Abstract

Affine processes possess the property that expectations of exponential affine transformations are given by a set of Riccati differential equations, which is the main feature of this popular class of processes. In this paper we generalise these results for expectations of more general transformations. This is of interest in, e.g. doubly stochastic Markov models, in particular in life insurance. When using affine processes for modelling the transition rates and interest rate, the results presented allow for easy calculation of transition probabilities and expected present values.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2016 

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References

[1]Biffis, E. (2005).Affine processes for dynamic mortality and actuarial valuations.Insurance Math. Econom. 37,443468.CrossRefGoogle Scholar
[2]Buchardt, K. (2014).Dependent interest and transition rates in life insurance.Insurance Math. Econom. 55,167179.CrossRefGoogle Scholar
[3]Dahl, M. (2004).Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts.Insurance Math. Econom. 35,113136.CrossRefGoogle Scholar
[4]Dahl, M. and Møller, T. (2006).Valuation and hedging of life insurance liabilities with systematic mortality risk.Insurance Math. Econom. 39,193217.CrossRefGoogle Scholar
[5]Duffie, D.,Pan, J. and Singleton, K. (2000).Transform analysis and asset pricing for affine jump-diffusions.Econometrica 68,13431376.CrossRefGoogle Scholar
[6]Filipović, D. (2005).Time-inhomogeneous affine processes.Stoch. Process. Appl. 115,639659.CrossRefGoogle Scholar
[7]Filipović, D. (2009).Term-Structure Models.Springer,Berlin.CrossRefGoogle Scholar
[8]Jarrow, R. A.,Lando, D. and Turnbull, S. M. (1997).A Markov model for the term structure of credit risk spreads.Rev. Financial Stud. 10,481523.CrossRefGoogle Scholar
[9]Kraft, H. and Steffensen, M. (2007).Bankruptcy, counterparty risk, and contagion.Rev. Finance 11,209252.CrossRefGoogle Scholar
[10]Lando, D. (1998).On Cox processes and credit risky securities.Rev. Derivatives Res. 2,99120.CrossRefGoogle Scholar
[11]Møller, T. and Steffensen, M. (2007).Market-Valuation Methods in Life and Pension Insurance.Cambridge University Press.CrossRefGoogle Scholar
[12]Norberg, R. (1999).A theory of bonus in life insurance.Finance Stoch 3,373390.CrossRefGoogle Scholar
[13]Schrager, D. F. (2006).Affine stochastic mortality.Insurance Math. Econom. 38,8197.CrossRefGoogle Scholar
[14]Wilmott, P. (2006).Paul Wilmott on Quantitative Finance,2nd edn.John Wiley,Chichester.Google Scholar

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