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Continuous affine processes: transformations, Markov chains and life insurance

Part of:Markov processesMathematical financeMathematical modeling, applications of mathematics

Published online by Cambridge University Press:  10 June 2016

Kristian Buchardt
Kristian Buchardt*
Affiliation:
University of Copenhagen and PFA Pension
*
* Postal address: PFA Pension, Sundkrogsgade 4, DK-2100 Copenhagen O, Denmark. Email address: kristian@buchardt.net
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Abstract

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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.

Keywords

Doubly stochastic processmulti-state life insurance modelscredit riskstochastic mortalitystochastic interest

MSC classification

Primary:97M30: Financial and insurance mathematics
Secondary:60J60: Diffusion processes91G40: Credit risk91G30: Interest rates (stochastic models)

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 2 , June 2016, pp. 423 - 442
Copyright
Copyright © Applied Probability Trust 2016 

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