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-559fc8cf4f-67gxp Total loading time: 0.345 Render date: 2021-03-05T18:21:49.814Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }
EnglishFrançais
Journal of Applied Probability Journal of Applied Probability

Article contents

Two results on dynamic extensions of deviation measures

Part of: Stochastic analysis Mathematical economics

Published online by Cambridge University Press:  16 July 2020

Mitja Stadje
Mitja Stadje
Affiliation:
Ulm University
Corresponding
E-mail address:
mitja.stadje@uni-ulm.de
Get access
Rights & Permissions[Opens in a new window]

Abstract

We give a dynamic extension result of the (static) notion of a deviation measure. We also study distribution-invariant deviation measures and show that the only dynamic deviation measure which is law invariant and recursive is the variance.

Keywords

Deviation measure time consistency law invariance

MSC classification

Primary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Secondary: 91B30: Risk theory, insurance 91B06: Decision theory 91B70: Stochastic models
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 2 , June 2020 , pp. 531 - 540
Copyright
© Applied Probability Trust 2020

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

Artzner, Ph., Delbaen, F., Eber, J.-M. and Heath, D. (1999). Coherent measures of risk. Math. Finance 9, 203–228.10.1111/1467-9965.00068CrossRefGoogle Scholar
Artzner, Ph., Delbaen, F., Eber, J.-M., Heath, D. and Ku, H. (2004). Coherent multiperiod risk adjusted values and Bellmans principle. Ann. Operat. Res. 152, 5–22.10.1007/s10479-006-0132-6CrossRefGoogle Scholar
Cheridito, P., Delbaen, F. and Kupper, M. (2006). Dynamic monetary risk measures for bounded discrete-time processes. Electron. J. Prob. 11, 57–106.10.1214/EJP.v11-302CrossRefGoogle Scholar
Delbaen, F., Peng, S. and Rosazza Gianin, E. (2010). Representation of the penalty term of dynamic concave utilities. Finance Stoch. 14, 449–472.10.1007/s00780-009-0119-7CrossRefGoogle Scholar
Elliott, R. J., Siu., T. K. and Cohen, S. N. (2015). Backward stochastic difference equations for dynamic convex risk measures on a binomial tree. J. Appl. Prob. 52, 771–785.10.1239/jap/1445543845CrossRefGoogle Scholar
Föllmer, H. and Schied, A. (2002). Convex measures of risk and trading constraints. Finance Stoch. 6, 429–447.10.1007/s007800200072CrossRefGoogle Scholar
Frittelli, M. and Rosazza Gianin, E. (2002). Putting order in risk measures. J. Bank. Finance 26, 1473–1486.10.1016/S0378-4266(02)00270-4CrossRefGoogle Scholar
Gerber, H. U. (1974). On iterative premium calculation principles. Sonderabdruck aus den Mitteilungen der Vereinigung schweizerischer Versicherungsmathematiker 74, 2.Google Scholar
Goovaerts, M. J.De Vylder, F. (1979). A note on iterative premium calculation principles. Astin Bull. 10, 325–329.10.1017/S0515036100005961CrossRefGoogle Scholar
Kaluszka, M. and Krzeszowiec, M. (2013). On iterative premium calculation principles under Cumulative Prospect Theory. Insurance Math. Econom. 52, 435–440.10.1016/j.insmatheco.2013.02.009CrossRefGoogle Scholar
Klöppel, S. and Schweizer, M. (2007). Dynamic indifference valuation via convex risk measures. Math. Finance 17, 599–627.CrossRefGoogle Scholar
Kupper, M. and Schachermayer, W. (2009). Representation results for law invariant time consistent functions. Math. Finan. Econom. 2, 189–210.10.1007/s11579-009-0019-9CrossRefGoogle Scholar
Pelsser, A. and Stadje, M. (2014). Time-consistent and market-consistent evaluation. Math. Finance 24, 25–62.10.1111/mafi.12026CrossRefGoogle Scholar
Pistorius, M. and Stadje, M. (2017). On dynamic deviation measures and continuous-time portfolio optimization. Ann. Appl. Prob. 27, 3342–3384.CrossRefGoogle Scholar
Rockafellar, R. T., Uryasev, S. P. and Zabarankin, M. (2002). Deviation measures in risk analysis and optimization. Working Paper 2002-7, Department of Industrial & Systems Engineering, University of Florida.Google Scholar
Rockafellar, R. T., Uryasev, S. P. and Zabarankin, M. (2006). Master funds in portfolio analysis with general deviation measures. J. Banking 30, 743–778.10.1016/j.jbankfin.2005.04.004CrossRefGoogle 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: 6
Total number of PDF views: 39 *
View data table for this chart

* Views captured on Cambridge Core between 16th July 2020 - 5th March 2021. This data will be updated every 24 hours.

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.

Two results on dynamic extensions of deviation measures
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.

Two results on dynamic extensions of deviation measures
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.

Two results on dynamic extensions of deviation measures
Available formats
×
×

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *