一类由广义g-期望诱导的相干风险度量及其表示定理
A Class of Coherent Measures of Risk via Generalized g-expectation and its Representation Theorem
摘要
本文通过广义g-期望引入了一类风险度量ρg,并在:g=-rtg-μ|z|时给出了相干风险度量ρg的表示定理。
This paper introduces a new class of risk measures ρg via generalized g-expectation and establishes a representation theorem for ρg when g=-rty-μ|z|
出处
《工程数学学报》
CSCD
北大核心
2005年第2期235-243,共9页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(10131030)
关键词
倒向随机微分方程
G-期望
广义g-期望
相干风险度量
GIRSANOV变换
backward stochastic differential equation
g-expectation
generalized g-expectation
coherent measures of risk
girsanov transformation
参考文献8
-
1Artzner P, Delbaen F, Eber J M, Heath D. Coherent measure of risk[J]. Mathematical Finance,1999;9(3) :203-228.
-
2Follmer H, Schied A. Convex measures of risk and trading constraints[J]. Finance and Stochastics,2002;6(4):429-447.
-
3Rossaza G E. Some examples of risk measures via g-expectations[R]. Working paper, University di Bergamo,Italy, 2003.
-
4Pardoux E, Peng S. Adapted solution of a backward stochastic differential equation[J]. Systems Control Letters, 1990; 14(1): 55-61.
-
5Peng S. BSDE and related g-expectations[A]. Pitman Research Notes in Mathematics Series, No.364, "Backward Stochastic Differential Equations" [C]. Harlow: Addison Welsey Longman, 1997, 141-159.
-
6El Karoui N, Peng S, Quenez M C. Backward stochastic differential equation in finance[J]. Mathematical Finance, 1997; 7(1): 1-71.
-
7Karatzas I, Shreve S E. Brownian motion and Stochastic Calculus[M]. 2nd edition. New York: SpringerVerlag, 1991.
-
8Coquet F, Hu Y, Memin J, Peng S. Filtration consistent nonlinear expectations and related g-expectation[J].Probab Theory and Related Fields, 2002;123(1):1-27.
