Back to Search
Start Over
Time consistent dynamic risk processes
- Source :
- Stochastic Processes and their Applications. (2):633-654
- Publisher :
- Elsevier B.V.
-
Abstract
- 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 cadlag 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 cadlag paths, and allowing for jumps, are exhibited.
- Subjects :
- Statistics and Probability
Mathematical optimization
Stochastic process
Applied Mathematics
Dynamic risk measures
Snell envelope
BMO martingales
Dynamic risk measure
Time consistency
Modeling and Simulation
Bounded function
Modelling and Simulation
Penalty method
Martingale (probability theory)
Random variable
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 03044149
- Issue :
- 2
- Database :
- OpenAIRE
- Journal :
- Stochastic Processes and their Applications
- Accession number :
- edsair.doi.dedup.....5ceb2aa237d2af103a479c97857d2fe9
- Full Text :
- https://doi.org/10.1016/j.spa.2008.02.011