# Igor Evstigneev (Manchester) - Von Neumann-Gale dynamical systems and their applications

Dates: | 18 November 2019 |
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Times: | 15:00 - 16:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Adults, Alumni, Current University students |

Speaker: | Igor Evstigneev |

Igor Evstigneev (Economics Department, University of Manchester) will be speaking at this research seminar, part of the Dynamical Systems and Analysis seminar series.

Abstract: Von Neumann-Gale dynamical systems are defined in terms of multivalued operators possessing properties of convexity and homogeneity. These operators assign to each element of a given cone a convex subset of the cone describing possible one-step transitions from one state of the system to another. The classical, deterministic theory of such dynamics was originally aimed at the modelling of economic growth (von Neumann 1937 and Gale 1956). Key results on von Neumann-Gale dynamical systems may be regarded as multivalued nonlinear versions of the Perron-Frobenius theorem on eigenvectors and eigenvalues of positive matrices. First attempts to build a stochastic generalization of this theory were undertaken in the 1970s by Dynkin, Radner and their research groups. However, the initial attack on the problem left many questions unanswered. Substantial progress was made only in the late 1990s, and final solutions to the main open problems were obtained only in the last decade. At about the same time it was observed that stochastic analogues of von Neumann-Gale dynamical systems provide a natural and convenient framework for financial modelling (asset pricing and hedging under transaction costs). This observation gave a new momentum to studies in the field and posed interesting new questions. The talk will review this area of research, emphasising recent achievements related to mathematical finance.

### Speaker

Igor Evstigneev