The dynamic programming equation for second order stochastic target problems

SIAM Journal on Control and Optimization

Volumn 48, Issue 4, 2009, Pages 2344-2365

  Soner, H Mete ^a   Touzi, Nizar ^b  

^a SABANCI UNIVERSITY   (Turkey)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

Gamma process; Geometric dynamic programming; Stochastic target problem; Viscosity solutions

Indexed keywords

DYNAMIC PROGRAMMING EQUATIONS; GAMMA PROCESS; SECOND ORDERS; STOCHASTIC TARGET PROBLEMS; VISCOSITY SOLUTIONS;

EID: 77954539667     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/07071130X     Document Type: Article

References (18)

1. P. BANK and D. BAUM, Hedging and portfolio optimization in financial markets with a large trader, Math. Finance, 14 (2004), pp. 1-18.
2. B. BOUCHARD, Stochastic targets with mixed diffusion processes and viscosity solutions, Stochastic Process. Appl., 101 (2002), pp. 273-302.
3. U. CETIN, H. M. SONER, and N. TOUZI, Options hedging for small investors under liquidity costs, Finance Stoch., to appear.
4. P. CHERIDITO, H. M. SONER, and N. TOUZI, The multi-dimensional super-replication problem under gamma constraints, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 (2005), pp. 633-666.
5. P. CHERIDITO, H. M. SONER, and N. TOUZI, Small time path behavior of double stochastic integrals and applications to stochastic control, Ann. Appl. Probab., 15 (2005), pp. 2472-2495.
6. P. CHERIDITO, H. M. SONER, N. TOUZI, and N. VICTOIR, Second order BSDE's and fully nonlinear PDE's, Comm. Pure Appl. Math., 60 (2007), pp. 1081-1110.
7. M. G. CRANDALL, H. ISHII, and P. L. LIONS, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., 27 (1992), pp. 1-67.
8. N. EL KAROUI, S. PENG, and M. C. QUENEZ, Backward stochastic differential equations in finance, Math. Finance, 7 (1997), pp. 1-71.
9. W. H. FLEMING and H. M. SONER, Controlled Markov Processes and Viscosity Solutions, Appl. Math. (N.Y.) 25, Springer-Verlag, New York, 1993.
10. N. IKEDA and S. WATANABE, Stochastic Differential Equations and Diffusion Processes, 2nd ed., North-Holland, Amsterdam, 1989.
11. I. KARATZAS and S. SHREVE, Brownian Motion and Stochastic Calculus, 2nd ed., Springer Verlag, New York, 1991.
12. S. LEVENTAL and A. V. SKOROHOD, On the possibility of hedging options in the presence of transaction costs, Ann. Appl. Probab., 7 (1997), pp. 410-443.
13. E. PARDOUX and S. PENG, Adapted solution of a backward stochastic differential equation, Systems Control Lett., 14 (1990), pp. 55-61.
14. S. PENG, Probabilistic interpretation for systems of quasilinear parabolic partial differential equations, Stochastics Stochastics Rep., 37 (1991), pp. 61-74.
15. N. SANTIER, General stochastic target problem with jump diffusion and application to hedging problem for large investor, Electron. Comm. Probab., 12 (2007), pp. 106-119.
16. H. M. SONER and N. TOUZI, Superreplication under gamma constraints, SIAM J. Control Optim., 39 (2000), pp. 73-96.
17. H. M. SONER and N. TOUZI, Stochastic target problems, dynamic programming, and viscosity solutions, SIAM J. Control Optim., 41 (2002), pp. 404-424.
18. H. M. SONER and N. TOUZI, Dynamic programming for stochastic target problems and geometric flows, J. Eur. Math. Soc. (JEMS), 8 (2002), pp. 201-236.