General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions

Qi Lü, Xu Zhang (Autoren)

Buch | Softcover

IX, 146 Seiten

2014
Springer International Publishing (Verlag)
978-3-319-06631-8 (ISBN)

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The classical Pontryagin maximum principle (addressed to deterministic finite dimensional control systems) is one of the three milestones in modern control theory. The corresponding theory is by now well-developed in the deterministic infinite dimensional setting and for the stochastic differential equations. However, very little is known about the same problem but for controlled stochastic (infinite dimensional) evolution equations when the diffusion term contains the control variables and the control domains are allowed to be non-convex. Indeed, it is one of the longstanding unsolved problems in stochastic control theory to establish the Pontryagin type maximum principle for this kind of general control systems: this book aims to give a solution to this problem. This book will be useful for both beginners and experts who are interested in optimal control theory for stochastic evolution equations.

1 Introduction.- 2 Preliminaries.- 3 Well-posedness of the vector-valued BSEEs.- 4 Well-posedness result for the operator-valued BSEEs with special data.- 5 Sequential Banach-Alaoglu-type theorems in the operator version.- 6 Well-posedness of the operator-valued BSEEs in the general case.- 7 Some properties of the relaxed transposition solutions to the operator-valued BSEEs.- 8 Necessary condition for optimal controls, the case of convex control domains.- 9 Necessary condition for optimal controls, the case of non-convex control domains.

Erscheint lt. Verlag	24.6.2014
Reihe/Serie	SpringerBriefs in Mathematics
Zusatzinfo	IX, 146 p. 1 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	250 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	Backward stochastics evolution equation • optimal control • Pontryagin-type maximum principle • Quantitative Finance • Stochastic Evolution Equations • Transportation solution
ISBN-10	3-319-06631-5 / 3319066315
ISBN-13	978-3-319-06631-8 / 9783319066318
Zustand	Neuware