Dans cette Note, nous donnons une condition nécessaire et suffisante sur g déterministe sous laquelle les g-espérances peut être représentée par les espérances de Choquet.
In this Note, we give a necessary and sufficient condition on deterministic g under which g-expectations can be represented as Choquet expectations.
Accepté le :
Publié le :
@article{CRMATH_2010__348_9-10_571_0, author = {Hu, Mingshang}, title = {On the integral representation of \protect\emph{g}-expectations}, journal = {Comptes Rendus. Math\'ematique}, pages = {571--574}, publisher = {Elsevier}, volume = {348}, number = {9-10}, year = {2010}, doi = {10.1016/j.crma.2010.04.008}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2010.04.008/} }
TY - JOUR AU - Hu, Mingshang TI - On the integral representation of g-expectations JO - Comptes Rendus. Mathématique PY - 2010 SP - 571 EP - 574 VL - 348 IS - 9-10 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2010.04.008/ DO - 10.1016/j.crma.2010.04.008 LA - en ID - CRMATH_2010__348_9-10_571_0 ER -
Hu, Mingshang. On the integral representation of g-expectations. Comptes Rendus. Mathématique, Tome 348 (2010) no. 9-10, pp. 571-574. doi : 10.1016/j.crma.2010.04.008. http://archive.numdam.org/articles/10.1016/j.crma.2010.04.008/
[1] A converse comparison theorem for BSDEs and related properties of g-expectation, Electronic Communications in Probability, Volume 5 (2000), pp. 101-117
[2] Choquet expectation and Peng's g-expectation, The Annals of Probability, Volume 33 (2005) no. 3, pp. 1179-1199
[3] Ambiguity, risk and asset returns in continuous time, Econometrica, Volume 70 (2002), pp. 1403-1443
[4] Minimax pricing and Choquet pricing, Insurance: Mathematics and Economics, Volume 38 (2006), pp. 518-528
[5] An integral representation theorem of g-expectations, Research Report INRIA, Volume 4284 (2001), pp. 1-20
[6] Theory of capacities, Ann. Inst. Fourier (Grenoble), Volume 5 (1953), pp. 131-195
[7] Filtration consistent nonlinear expectations and related g-expectations, Probability Theory and Related Fields, Volume 123 (2002), pp. 1-27
[8] Non-additive Measure and Integral, Kluwer Academic Publishers, Boston, 1994
[9] Backward stochastic differential equations in finance, Mathematical Finance, Volume 7 (1997), pp. 1-71
[10] Choquet expectations and g-expectations with multi-dimensional Brownian motion, 2009 (available via) | arXiv
[11] Convexity, translation invariance and subadditivity for g-expectations and related risk measures, Annals of Applied Probability, Volume 18 (2008) no. 1, pp. 245-258
[12] Adapted solution of a backward stochastic differential equation, Systems and Control Letters, Volume 14 (1990), pp. 55-61
[13] BSDE and stochastic optimizations, topics in stochastic analysis (Yan, J.; Peng, S.; Fang, S.; Wu, L.M., eds.), Lecture Notes of 1995 Summer School in Mathematics, Science Press, Beijing, 1997 Ch. 2 (Chinese vers.)
[14] Backward SDE related g-expectations, Backward stochastic differential equations (El Karoui, N.; Mazliak, L., eds.), Pitman Research Notes in Mathematics Series, vol. 364, Longman, Harlow, 1997, pp. 141-159
Cité par Sources :