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001 978-1-4614-4286-8
003 DE-He213
005 20140220082814.0
007 cr nn 008mamaa
008 120925s2013 xxu| s |||| 0|eng d
020 _a9781461442868
_9978-1-4614-4286-8
024 7 _a10.1007/978-1-4614-4286-8
_2doi
050 4 _aHB135-147
072 7 _aKF
_2bicssc
072 7 _aMAT003000
_2bisacsh
072 7 _aBUS027000
_2bisacsh
082 0 4 _a519
_223
100 1 _aTouzi, Nizar.
_eauthor.
245 1 0 _aOptimal Stochastic Control, Stochastic Target Problems, and Backward SDE
_h[electronic resource] /
_cby Nizar Touzi.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aX, 214 p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aFields Institute Monographs,
_x1069-5273 ;
_v29
505 0 _aPreface -- 1. Conditional Expectation and Linear Parabolic PDEs -- 2. Stochastic Control and Dynamic Programming -- 3. Optimal Stopping and Dynamic Programming -- 4. Solving Control Problems by Verification -- 5. Introduction to Viscosity Solutions -- 6. Dynamic Programming Equation in the Viscosity Sense -- 7. Stochastic Target Problems -- 8. Second Order Stochastic Target Problems -- 9. Backward SDEs and Stochastic Control -- 10. Quadratic Backward SDEs -- 11. Probabilistic Numerical Methods for Nonlinear PDEs -- 12. Introduction to Finite Differences Methods -- References.
520 _aThis book collects some recent developments in stochastic control theory with applications to financial mathematics. In the first part of the volume, standard stochastic control problems are addressed from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on regularity issues and, in particular, on the behavior of the value function near the boundary. Then a quick review of the main tools from viscosity solutions allowing one to overcome all regularity problems is provided.   The second part is devoted to 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 second order extension was motivated by illiquidity modeling, and the controlled loss version was introduced following the problem of quantile hedging.   The third part presents an overview of backward stochastic differential equations and their extensions to the quadratic case. Backward stochastic differential equations are intimately related to the stochastic version of Pontryagin’s maximum principle and can be viewed as a strong version of stochastic target problems in the non-Markov context. The main applications to the hedging problem under market imperfections, the optimal investment problem in the exponential or power expected utility framework, and some recent developments in the context of a Nash equilibrium model for interacting investors, are presented.   The book concludes with a review of the numerical approximation techniques for nonlinear partial differential equations based on monotonic schemes methods in the theory of viscosity solutions.
650 0 _aMathematics.
650 0 _aDifferential equations, partial.
650 0 _aFinance.
650 0 _aMathematical optimization.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aQuantitative Finance.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aPartial Differential Equations.
650 2 4 _aCalculus of Variations and Optimal Control; Optimization.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461442851
830 0 _aFields Institute Monographs,
_x1069-5273 ;
_v29
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-4286-8
912 _aZDB-2-SMA
999 _c95103
_d95103