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Bernt Øksendal, Badr-eddine Berrhazi, Erik Ekström

Välkommen till tre föreläsningar i seminarieserien i matematik.

Föreläsningarna är en del av workshopen Stochastics: a workshop on diffusion processes, BSDEs, optimal control, and risks.

Föreläsare/Lecturers

  • 13:00-13:40 Bernt Øksendal, Universitetet i Oslo, Norge
  • 13:40-14:00 Badr-eddine Berrhazi, Université Ibn Tofaïl, Marocko / Linnéuniversitetet
  • 14:15-14:55 Erik Ekström, Uppsala universitet

Titlar/Titles

  • Optimal control of stochastic Volterra integral equations
  • Reflected backward doubly stochastic differential equations with discontinuous barrier
  • Bayesian sequential least-squares estimation of the drift of a Wiener process

Sammanfattningar/Abstracts

  • Bernt Øksendal: Optimal control of stochastic Volterra integral equations
    We study optimal control of stochastic Volterra integral equations (SVIE) with jumps by using Hida-Malliavin calculus. We give conditions under which there exists a unique solution of such equations. Then we prove both a sufficient maximum principle (a verification theorem) and a necessary maximum principle via Hida-Malliavin calculus. As an application we solve a problem of optimal consumption from a cash flow modelled by an SVIE. The talk is based on joint work with Nacira Agram and Samia Yakhlef, University of Biskra, Algeria.
  • Badr-eddine Berrhazi: Reflected backward doubly stochastic differential equations with discontinuous barrier
    In this work we investigate reflected backward doubly stochastic differential equations (RBDSDEs) with a lower not necessarily right-continuous obstacle. First we establish the existence and uniqueness of a solution to RBDSDEs with Lipschitz drivers. In the second part we present a comparison theorem and we prove existence of a minimal solution to RBDSDEs with continuous driver.
  • Erik Ekström: Bayesian sequential least-squares estimation of the drift of a Wiener process
    Given a Wiener process with unknown and unobservable drift, we seek to estimate this drift as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a linear cost per unit time of observation. In a Bayesian framework, this question reduces to choosing judiciously a stopping time for an appropriate diffusion process in natural scale; we provide structural properties of the solution for the corresponding problem of optimal stopping.

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