Electronic Resource

Optimal stochastic control, stochastic target problems, and backward SDE

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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 second order 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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Ketersediaan

Informasi Detail

Judul Seri

Fields Institute monographs

No. Panggil

E463

Penerbit

New York : Springer., 2012

Deskripsi Fisik

x, 214 hlm.

Bahasa

English

ISBN/ISSN

9781461442868

Klasifikasi

NONE

Tipe Isi

text

Tipe Media

computer

Tipe Pembawa

online resource

Edisi

1

Subjek

Probabilitas dan Matematika Terapan
Kalkulus Variasi

Info Detail Spesifik

-

Pernyataan Tanggungjawab

Nizar Touzi

Versi lain/terkait

Lampiran Berkas

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