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portada Optimal Stochastic Control, Stochastic Target Problems, and Backward Sde
Type
Physical Book
Author
Publisher
Language
English
Pages
214
Format
Paperback
Dimensions
23.4x15.6x1.2 cm
Weight
0.32 kg.
ISBN13
9781493900428
Categories

Optimal Stochastic Control, Stochastic Target Problems, and Backward Sde

Nizar Touzi (Author) · Springer PG · Paperback

Optimal Stochastic Control, Stochastic Target Problems, and Backward Sde - Touzi, Nizar

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Synopsis "Optimal Stochastic Control, Stochastic Target Problems, and Backward Sde"

This book collects some recent developments in stochastic control theory with applications to financial mathematics. We first address standard stochastic control problems from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on the regularity issues and, in particular, on the behavior of the value function near the boundary. We then provide a quick review of the main tools from viscosity solutions which allow to overcome all regularity problems. We next address the class of stochastic target problems which extends in a nontrivial way the standard stochastic control problems. Here the theory of viscosity solutions plays a crucial role in the derivation of the dynamic programming equation as the infinitesimal counterpart of the corresponding geometric dynamic programming equation. The various developments of this theory have been stimulated by applications in finance and by relevant connections with geometric flows. Namely, the secondorder extension was motivated by illiquidity modeling, and the controlled loss version was introduced following the problem of quantile hedging. The third part specializes to an overview of Backward stochastic differential equations, and their extensions to the quadratic case.​

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