Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
  • Home
Hostname: page-component-78dcdb465f-f64jw Total loading time: 0.449 Render date: 2021-04-16T22:55:38.238Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }
EnglishFrançais
Advances in Applied Probability Advances in Applied Probability

Article contents

Continuous affine processes: transformations, Markov chains and life insurance

Part of: Mathematical finance Mathematical modeling, applications of mathematics Markov processes

Published online by Cambridge University Press:  10 June 2016

Kristian Buchardt
Kristian Buchardt
Affiliation:
University of Copenhagen and PFA Pension
Corresponding
E-mail address:
kristian@buchardt.net
Get access
Rights & Permissions[Opens in a new window]

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.

Keywords

Doubly stochastic process multi-state life insurance models credit risk stochastic mortality stochastic interest

MSC classification

Primary: 97M30: Financial and insurance mathematics
Secondary: 60J60: Diffusion processes 91G40: Credit risk 91G30: Interest rates (stochastic models)
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 2 , June 2016 , pp. 423 - 442
Copyright
Copyright © Applied Probability Trust 2016 

Access options

Get access to the full version of this content by using one of the access options below.
If you should have access and can't see this content please contact technical support.

References

[1]Biffis, E. (2005).Affine processes for dynamic mortality and actuarial valuations.Insurance Math. Econom. 37,443–468.CrossRefGoogle Scholar
[2]Buchardt, K. (2014).Dependent interest and transition rates in life insurance.Insurance Math. Econom. 55,167–179.CrossRefGoogle Scholar
[3]Dahl, M. (2004).Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts.Insurance Math. Econom. 35,113–136.CrossRefGoogle Scholar
[4]Dahl, M. and Møller, T. (2006).Valuation and hedging of life insurance liabilities with systematic mortality risk.Insurance Math. Econom. 39,193–217.CrossRefGoogle Scholar
[5]Duffie, D.,Pan, J. and Singleton, K. (2000).Transform analysis and asset pricing for affine jump-diffusions.Econometrica 68,1343–1376.CrossRefGoogle Scholar
[6]Filipović, D. (2005).Time-inhomogeneous affine processes.Stoch. Process. Appl. 115,639–659.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. 10,481–523.CrossRefGoogle Scholar
[9]Kraft, H. and Steffensen, M. (2007).Bankruptcy, counterparty risk, and contagion.Rev. Finance 11,209–252.CrossRefGoogle Scholar
[10]Lando, D. (1998).On Cox processes and credit risky securities.Rev. Derivatives Res. 2,99–120.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 3,373–390.CrossRefGoogle Scholar
[13]Schrager, D. F. (2006).Affine stochastic mortality.Insurance Math. Econom. 38,81–97.CrossRefGoogle Scholar
[14]Wilmott, P. (2006).Paul Wilmott on Quantitative Finance,2nd edn.John Wiley,Chichester.Google Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 65 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 16th April 2021. This data will be updated every 24 hours.

3
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Continuous affine processes: transformations, Markov chains and life insurance
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Continuous affine processes: transformations, Markov chains and life insurance
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Continuous affine processes: transformations, Markov chains and life insurance
Available formats
×
×

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *