Optimal controls with rough paths and Backward Stochastic Differential Equations

In this talk, we try to extend the classical optimal control theory, i.e. stochastic / deterministic maximizations, in the framework of rough paths. In real worlds, such as micro economics and material sciences, some phenomena cannot be fully described in the framework of the Semimartingale processes. The statistics from highly oscillating data in the finance, and the elasticity of fibers caused by its torsion tensors, are the examples of such cases. We would like to present a theoretical framework for optimizations of such problems, by using the theory of rough paths.

To solve the optimization, two ways exist traditionally: Backward Stochastic Differential Equations (BSDEs) and Hamilton-Jacobi-Bellman equations (HJBs). The latter requires the Markov property of the process in the interest. Here, we shall take the approach of BSDEs, by studying the Hamiltonian and the related duality in the optimization. We present a condition which enables us to extend the method of BSDEs in the framework of rough paths.

It was Professor Terry Lyons who first suggested me to consider BSDEs with rough paths.


Mariko Arisawa (Tohoku University)

Monday, March 18, 2013 - 14:00
to 15:00