The dynamic programming equation for second order stochastic target problems

Soner, Halil Mete and Touzi, Nizar (2009) The dynamic programming equation for second order stochastic target problems. SIAM Journal on Control and Optimization, 48 (4). pp. 2344-2365. ISSN 0363-0129 (print) 1095-7138 (online)

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Official URL: http://dx.doi.org/10.1137/07071130X


Motivated by applications in mathematical finance [U. Cetin, H. M. Soner, and N. Touzi, "Options hedging for small investors under liquidity costs," Finance Stoch., to appear] we continue our study of second order backward stochastic equations. In this paper, we derive the dynamic programming equation for a certain class of problems which we call the second order stochastic target problems. In contrast with previous formulations of similar problems, we restrict control processes to be continuous. This new framework enables us to apply our results to a larger class of models. Also the resulting derivation is more transparent. The main technical tool is the geometric dynamic programming principle in this context, and it is proved by using the framework developed in [H. M. Soner and N. Touzi, J. Eur. Math. Soc. (JEMS), 8 (2002), pp. 201-236].

Item Type:Article
Uncontrolled Keywords:stochastic target problem; gamma process; geometric dynamic programming; viscosity solutions
ID Code:13566
Deposited By:Halil Mete Soner
Deposited On:17 Dec 2009 21:13
Last Modified:24 Jul 2019 12:33

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