Nacira Agram: Forward/backward stochastic Volterra integral equations and related topics

V četrtek, 31. maja 2018, ob 14:15 bo v predavalnici 3.06 Fakultete za matematiko in fiziko Univerze v Ljubljani na Jadranski ulici 21 v Ljubljani potekalo predavanje Nacire Agram (University of Oslo) z naslovom Forward/backward stochastic Volterra integral equations and related topics.

Abstract: Stochastic Volterra integral equations are a special type of integral equations. They represent interesting models for stochastic dynamics with memory, with applications to e.g. engineering, biology and finance. Solutions of stochastic Volterra (integral) equations are not Markov processes, and therefore classical methods, like dynamic programming, cannot be used to study optimal control problems for such equations. However, we show that, by using Hida-Malliavin calculus, it is possible to formulate a modified functional type of maximum principle suitable for such systems. An adjoint process obtained will satisfy a backward stochastic Volterra integral equation with jumps. Interesting motivation for this type of equations arises from recursive utility and from dynamic risk measures. Since solutions of backward stochastic Volterra integral equations are not in general a semimartingales, we will discuss some particular cases.