Seminarium i matematik
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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