Time consistent dynamic risk processes
A crucial property for dynamic risk measures is the time consistency. In this paper, a characterization of time consistency in terms of a "cocycle condition" for the minimal penalty function is proved for general dynamic risk measures continuous from above. Then the question of the regularity of paths is addressed. It is shown that, for a time consistent dynamic risk measure normalized and non-degenerate, the process associated with any bounded random variable has a càdlàg modification, under a mild condition always satisfied in the case of continuity from below. When normalization is not assumed, a right continuity condition on the penalty has to be added. Applying these results and using right continuous BMO martingales, families of not necessarily normalized dynamic risk measures leading to càdlàg paths, and allowing for jumps, are exhibited.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 119 (2009)
Issue (Month): 2 (February)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description|
|Order Information:|| Postal: http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
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.:
- Riedel, Frank, 2004.
"Dynamic coherent risk measures,"
Stochastic Processes and their Applications,
Elsevier, vol. 112(2), pages 185-200, August.
- Frank Riedel, 2003. "Dynamic Coherent Risk Measures," Working Papers 03004, Stanford University, Department of Economics.
- Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
- Jocelyne Bion-Nadal, 2008. "Dynamic risk measures: Time consistency and risk measures from BMO martingales," Finance and Stochastics, Springer, vol. 12(2), pages 219-244, April.
- Roorda, Berend & Schumacher, J.M., 2007. "Time consistency conditions for acceptability measures, with an application to Tail Value at Risk," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 209-230, March.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Föllmer Hans & Penner Irina, 2006. "Convex risk measures and the dynamics of their penalty functions," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-36, July.
- Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
- Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. Full references (including those not matched with items on IDEAS)