Stochastic control with fixed marginal distributions

Preprint Series # 800
Mikami, Toshio Stochastic control with fixed marginal distributions. (2006);

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Abstract

We briefly describe the so-called Monge-Kantorovich Problem (MKP for short) which is often referred to as an optimal mass transportation problem and study the stochastic optimal control problem (SOCP for short) with fixed initial and terminal distributions. In particular, we study the so-called Duality Theorem for the SOCP where continuous semimartingales under consideration have a variable diffusion matrix and then discuss the relation between the MKP and the SOCP. We also study the so-called Nelson's Problem, as the SOCP with fixed marginal distributions at each time, to which we give a new approach from the Duality Theorem. We finally consider a class of deterministic variational problems with fixed marginal distributions which is related to the SOCP by extending a class of measures under consideration.

Item Type: Preprint 15 copies Monge-Kantorovich Problem, Stochastic control, fixed marginal distributions Nelson's Problem,Duality Theorem 93-xx SYSTEMS THEORY; CONTROL 1610