## Applied Stochastic Control of Jump DiffusionsIn this second edition, we have added a chapter on optimal control of random jump ?elds (solutions of stochastic partial di?erential equations) and partial information control (Chap.10). We have also added a section on optimal st- ping with delayed information (Sect.2.3). It has always been our intention to give a contemporary presentation of applied stochastic control, and we hope thattheadditionoftheserecentdevelopmentswillcontributeinthisdirection. Wehavealsomadeanumberofcorrectionsandotherimprovements,many of them based on helpful comments from our readers. In particular, we would like to thank Andreas Kyprianou for his valuable communications. We are also grateful to (in alphabetical order) Knut Aase, Jean-Philippe Chancelier, Inga Eide, Emil Framnes, Arne-Christian Lund, Jose-Luis Menaldi, Tam ́ as K. Papp, Atle Seierstad, and Jens Arne Sukkestad for pointing out errors and suggesting improvements. Our special thanks go to Martine Verneuille for her skillful typing. Oslo and Paris, November 2006 Bernt Øksendal and Agn` es Sulem Preface of the First Edition Jump di?usions are solutions of stochastic di?erential equations driven by L ́ evy processes. Since a L ́ evy process ?(t) can be written as a linear com- nation of t, a Brownian motion B(t) and a pure jump process, jump di- sions represent a natural and useful generalization of Itˆ o di?usions. They have received a lot of attention in the last years because of their many applications, particularly in economics. |

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### Contents

Stochastic Calculus with Jump Diffusions | 1 |

Optimal Stopping of Jump Diffusions | 27 |

Stochastic Control of Jump Diffusions | 45 |

Copyright | |

9 other sections not shown

### Other editions - View all

Applied Stochastic Control of Jump Diffusions Bernt Øksendal,Agnès Sulem-Bialobroda Limited preview - 2007 |

Applied Stochastic Control of Jump Diffusions Bernt Øksendal,Agnès Sulem-Bialobroda Limited preview - 2006 |

Applied Stochastic Control of Jump Diffusions Bernt Øksendal,Agnes Sulem-Bialobroda Limited preview - 2004 |

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0ksendal adB(t admissible controls Algebra apply assume Brownian motion cadlag Chap choose combined control conditions of Theorem consider constants continuation region corresponding dB(t Define denote dX(t dY(t dynamic programming Dynkin formula e-psip(x Example exists finite geometric Levy process Geometry Girsanov Theorem guess Hence HJBQVI holds impulse control impulse control problem intervention ip(x Ito formula Ito-Levy process jump diffusion Lemma Let X(t Levy process Linear ln(l Markov martingale martingale with respect maximum principle Moreover optimal consumption optimal control optimal stopping problem Poisson Poisson random measure portfolio process Y(t proof of Theorem prove satisfies singular control solve stochastic control problem Stochastic Differential Equations sup Ey Suppose Theorem 2.2 Theory tp(x Transaction Costs uniformly integrable unique v(dz value function variational inequalities verification theorem viscosity solution viscosity subsolution viscosity supersolution zN(dt,dz