Numerical methods for stochastic control problems in continuous time. 2nd ed.

*(English)*Zbl 0968.93005
Applications of Mathematics. 24. New York, NY: Springer. xii, 475 p. (2001).

In this second edition [for the first edition see (1992; Zbl 0754.65068)], the main change is a new chapter thirteen inserted between chapter twelve and thirteen of the previous version and the old chapter thirteen has been split into two chapters which consider deterministic problems from the point of view of the calculus of variations with finite and infinite horizon, respectively.

Chapter thirteen considers problems which have attracted the attention of research recently namely the cases of controlled variance (with applications in finance) and controlled jumps (with applications in communication). In order to obtain convergence, one has to enlarge the driving Wiener (resp. Poisson) processes by introducing the martingale measure (resp. relaxed Poisson measure).

Chapter thirteen considers problems which have attracted the attention of research recently namely the cases of controlled variance (with applications in finance) and controlled jumps (with applications in communication). In order to obtain convergence, one has to enlarge the driving Wiener (resp. Poisson) processes by introducing the martingale measure (resp. relaxed Poisson measure).

Reviewer: A.Akutowicz (Berlin)

##### MSC:

93-02 | Research exposition (monographs, survey articles) pertaining to systems and control theory |

93E20 | Optimal stochastic control |

65K10 | Numerical optimization and variational techniques |

90C39 | Dynamic programming |

65C40 | Numerical analysis or methods applied to Markov chains |

93E25 | Computational methods in stochastic control (MSC2010) |

60J22 | Computational methods in Markov chains |

60J75 | Jump processes (MSC2010) |