Time consistent dynamic risk processes

被引:50
作者
Bion-Nadal, Jocelyne [1 ]
机构
[1] Ecole Polytech, CMAP UMR CNRS 7641, F-91128 Palaiseau, France
关键词
Dynamic risk measures; Time consistency; BMO martingales; Snell envelope;
D O I
10.1016/j.spa.2008.02.011
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
070103 [概率论与数理统计]; 140311 [社会设计与社会创新];
摘要
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. (C) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码:633 / 654
页数:22
相关论文
共 28 条
[1]
[Anonymous], 557 CMAP
[2]
[Anonymous], 1980, PROBABILITES POTENTI
[3]
[Anonymous], RISK MEASURES 21 CEN
[4]
[Anonymous], 1965, Holden-Day Series in Probability and Statistics
[5]
[Anonymous], 1994, LECT NOTES MATH
[6]
Coherent measures of risk [J].
Artzner, P ;
Delbaen, F ;
Eber, JM ;
Heath, D .
MATHEMATICAL FINANCE, 1999, 9 (03) :203-228
[7]
Coherent multiperiod risk adjusted values and Bellman's principle [J].
Artzner, Philippe ;
Delbaen, Freddy ;
Eber, Jean-Marc ;
Heath, David ;
Ku, Hyejin .
ANNALS OF OPERATIONS RESEARCH, 2007, 152 (1) :5-22
[8]
BARRIEU P, VOLUME INDI IN PRESS
[9]
Dynamic risk measures: Time consistency and risk measures from BMO martingales [J].
Bion-Nadal, Jocelyne .
FINANCE AND STOCHASTICS, 2008, 12 (02) :219-244
[10]
BIONNADAL J, 2007, 613 CMAP