Work

Optimal bilinear control of nonlinear stochastic Schrödinger equations driven by linear multiplicative noise

Year: 2018

Type: article

Abstract: We analyze the bilinear optimal control problem of quantum mechanical systems with final observation governed by a stochastic nonlinear Schrödinger equation perturbed by a linear multiplicative Wiener process. The existence of an open-loop optimal control and first-order Lagrange optimality conditions are derived, via Skorohod’s representation theorem, Ekeland’s variational principle and the existence for the linearized dual backward stochastic equation. Moreover, our approach in particular applies to the deterministic case.

Source: The Annals of Probability

DOI: 10.1214/17-aop1217

Authors: Viorel Barbu, Michael Röckner, Deng Zhang

Institutions: Alexandru Ioan Cuza University, Shanghai Jiao Tong University, Bielefeld University, Romanian Academy

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze