Convexity, translation invariance and subadditivity for g-expectations and related risk measures

Annals of Applied Probability

Volumn 18, Issue 1, 2008, Pages 245-258

  Jiang, Long ^a  

^a CHINA UNIVERSITY OF MINING AND TECHNOLOGY   (China)

Author keywords

Backward stochastic differential equation; Convexity of g expectation; G expectation; Risk measure; Translation invariance of g expectation

Indexed keywords

EID: 53349179624     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/105051607000000294     Document Type: Article

References (21)

1. ARTZNER, P., DELBAEN, F., EBER, J. M. and HEATH, D. (1999). Coherent measures of risk, Math. Finance 4 203-228. MR1850791
2. BARRIEU, P. and EL KAROUI, N. (2004). Optimal derivatives design under dynamic risk measures. In Mathematics of Finance (G. Yin and Q. Zhang, eds.) 13-25. Amer. Math. Soc., Providence, RI. MR2076287
3. BRIAND, PH., COQUET, F., HU, Y., MÉMIN, J. and PENG, S. (2000). A converse comparison theorem for BSDEs and related properties of g-expectation. Electron. Comm. Probab. 5 101-117. MR1781845
4. CHEN, Z., CHEN, T. and DAVISON, M. (2005). Choquet expectation and Peng's g-expectation. Ann. Probab. 33 1179-1199. MR2135317
5. CHEN, Z. and EPSTEIN, L. (2002). Ambiguity, risk and asset returns in continuous time. Econometrica 70 1403-1444. MR1929974
6. COQUET, F., HU, Y., MÉMIN, J. and PENG, S. (2002). Filtration consistent nonlinear expectations and related g-expectation. Probab. Theory Related Fields 123 1-27. MR1906435
7. CVITANIC, J. and KARATZAS, I. (1999). On dynamic measures of risk. Finance Stoch 3 451-482. MR1842283
8. EL KSAROUI, N., PENG, S. and QUENEZ, M. C. (1997). Backward stochastic differential equations in finance. Math. Finance 7 1-71. MR1434407
9. FÖLLMER, H. and SCHIED, A. (2002). Convex measures of risk and trading constraints. Finance Stock. 6 429-447. MR1932379
10. FÖLLMER, H. and SCHIED, A. (2002). Stochastic Finance, an Introduction in Discrete Time. De Gruyter, Berlin-New York. MR1925197
11. FRITTELLI, M. and ROSAZZA GIANIN, E. (2002). Putting order in risk measures. J. Banking and Finance 26 1473-1486.
12. HEWITT, E. and STROMBERG, K. R. (1978). Real and Abstract Analysis. Springer, New York. MR0367121
13. JIANG, L. (2004). Some results on the uniqueness of generators of backward stochastic differential equations. C. R. Acad. Sci. Paris Sér. I 338 575-580. MR2057033
14. JIANG, L. (2005). Nonlinear expectation - g-expectation theory and its applications in finance. Ph. D. thesis, Shandong Univ., P. R. China.
15. JIANG, L. (2005). Representations theorems for generators of backward stochastic differential equations and their applications. Stock Process. Appl. 115 1883-1903. MR2178500
16. PARDOUX, E. and PENG, S. (1990). Adapted solution of a backward stochastic differential equation. Syst. Control. Lett. 14 55-61. MR1037747
17. PENG, S. (1997). Backward SDE and related g-expectation. In Backward Stochastic Differential Equations (N. El Karoui and L. Mazliak, eds.). Pitman Research Notes Math. Ser. 364 141-159. Longman, Harlow. MR1752680
18. PENG, S. (1999). Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer's type. Probab. Theory Related Fields 113 473-499. MR1717527
19. PENG, S. (2004). Nonlinear expectations, nonlinear evaluations and risk measures. Stochastic Methods in Finance Lectures. Lecture Notes in Math. 1856 143-217. Springer, Berlin. MR2113723
20. ROSAZZA GIANIN, E. (2002). Convexity and law invariance of risk measures. Ph. D. thesis, Univ. di Bergamo, Italy.
21. ROSAZZA GIANIN, E. (2006). Risk measures via g-expectations. Insurance: Mathematics and Economics 39 19-34. MR2241848