BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations

Stochastic Processes and their Applications

Volumn 107, Issue 1, 2003, Pages 145-169

  El Karoui, N ^a   Hamadene S ^b  

^a ECOLE POLYTECHNIQUE   (France)

^b UNIVERSITÉ DU MAINE   (France)

Author keywords

Backward SDEs; Equilibrium point; Nonzero sum game; Optimal control; Risk sensitive control; Saddle point; Zero sum game

Indexed keywords

EID: 0042843669     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(03)00059-0     Document Type: Article

References (31)

1. Barrieu P. El-Karoui N. Optimal design of derivatives in illiquid markets Quantitat. Finance 2 2002 181-188
2. Barrieu, P., El-Karoui, N., 2002b. Optimal design of derivatives and Quadratic BSDEs with non tradable risk. Preprint CMAP, Ecole Polytechnique.
3. Benes V.E. Existence of optimal strategies based on specified information for a class of stochastic decision problems SIAM J. Control Optim. 8 1970 179-188
4. Bensoussan A. Perturbation Methods in Optimal Control 1988 Bordas/Wiley Paris/New York
5. Bensoussan A. Nagai H. Min-max characterization of a small noise limit on risk-sensitive control SIAM J. Control Optim. 35 4 1997 1093-1115
6. Bensoussan A. Frehse J. Nagai H. Some results on risk-sensitive with full observation J. Appl. Math. Optim. 37 1 1998 1-41
7. Bertsekas D.P. Dynamic Programming and Stochastic Control 1976 Academic Press New York
8. Buckdahn, R., Hu, Y., 1998. Hedging contingent claims for a large investor in an incomplete market. Adv. Appl. Probab. 30, 239-255.
9. Cvitanic J. Karatzas I. Backward SDEs with reflection and Dynkin games Ann. Probab. 24 4 1996 2024-2056
10. Davis M.H.A. Varaiya P. Dynamic programming conditions for partially observable stochastic systems SIAM J. Control Optim. 11 2 1973 226-261
11. Dupuis P. McEneaney W.M. Risk-sensitive and robust escape criteria SIAM J. Control Optim. 35 6 1996 2021-2049
12. El-Karoui N. Peng S. Quenez M.-C. Backward stochastic differential equations in Finance Math. Finance 7 1997 1-71
13. Fleming W.H. McEneaney W.M. Risk-sensitive control on an infinite time horizon SIAM J. Control Optim. 33 6 1995 1881-1915
14. Fleming, W.H., Sheu, S.J., 2002. Risk-sensitive control and an optimal investment model (II). Preprint.
15. Girsanov I.V. On transforming a certain class of stochastic processes by absolutely continuous substitution of measures Theory Probab. Appl. 5 1960 285-301
16. Hamadène S. Lepeltier J.P. Zero-sum stochastic differential games and backward equations Systems Control Lett. 24 1995 259-263
17. Hamadène S. Lepeltier J.P. Backward equations, stochastic control and zero-sum stochastic differential games Stochastics and Stochastic Reports 54 1995 221-231
18. Hamadène S. Lepeltier J.P. Peng S. BSDE with continuous coefficients and application to Markovian non-zero sum stochastic differential games In: El-Karoui N. Mazliak L. (Eds.), Pitman Research Notes in Mathematics Series Vol. 364 1997 115-128 Longman Harlow
19. Jacobson D.H. Optimal stochastic linear systems with exponential criteria and their relation to differential games IEEE Trans. Automat. Control AC-18 1973 124-131
20. Karatzas I. Shreve S.E. Brownian Motion and Stochastic Calculus 1991 Springer New York
21. Kobylanski M. Backward stochastic differential equations and partial differential equations with quadratic growth Ann. Probab. 28 2000 558-602
22. Kuroda, K., Nagai, H., 2002. Risk-sensitive portfolio optimization on infinite time horizon. Stochastics and Stochastic Reports, 309-331.
23. Lepeltier J.P. Marchal B. Sur l'existence de politiques optimales dans le contrôle integro-différentiel Ann. Inst. H. Poincaré XIII 1 1977 45-97
24. Lepeltier J.P. San Martin J. Existence for BSDE with superlinear quadratic coefficient Stochastics Stochastic Rep. 63 1998 227-240
25. Nagai H. Bellmann equations of risk-sensitive control SIAM J. Control Optim. 34 1 1996 74-101
26. Pardoux E. BSDEs, weak convergence and homogenization of semilinear PDEs In: Clarke F. Stern R. (Eds.), Nonlinear Analysis, Differential Equations and Control 1999 503-549 Kluwer Academic Netherlands
27. Pardoux E. Peng S. Adapted solutions of backward stochastic differential equations Systems and Control Letters 14 1990 51-61
28. Pardoux E. Peng S. Backward stochastic differential equations and quasilinear parabolic partial differential equations In: Rozovskii B. Sowers R. (Eds.), Stochastic Differential Equations and their Applications Lecture Notes in Control and Information Science Vol. 176 1992 200-217 Springer Berlin
29. Peng S. Probabilistic interpretation for systems of quasilinear parabolic partial differential equations Stochastics 14 1991 61-74
30. Revuz D. Yor M. Continuous Martingales and Brownian Motion 1991 Springer Berlin
31. Whittle P. Risk-sensitive linear quadratic gaussian control Adv. Appl. Prob. 13 1974 764-767