Stochastic control with fixed marginal distributions

Mikami, Toshio

Hokkaido University Preprint Series in Mathematics, 2006, 800, 1-48

Permalink : https://doi.org/10.14943/83950

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アクセス権	open access
DOI	https://doi.org/10.14943/83950
URI	https://hdl.handle.net/2115/69608
タイトル	Stochastic control with fixed marginal distributions
著者	著者名 Mikami, Toshio
言語	英語
キーワード	Monge-Kantorovich Problem
	Stochastic control
	fixed marginal distributions Nelson's Problem,Duality Theorem
発行日	2006-08-24
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	800
ページ	1-48
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record