Year: 2015
Type: conference-paper
Abstract: Exploiting a fluid dynamic formulation for which a probabilistic counterpart might not be available, we extend the theory of Schrödinger bridges to the case of inertial particles with losses and general, possibly singular diffusion coefficient. We find that, as for the case of constant diffusion coefficient matrix, the optimal control law is obtained by solving a system of two p.d.e.'s involving adjoint operators and coupled through their boundary values. In the linear case with quadratic loss function, the system turns into two matrix Riccati equations with coupled split boundary conditions. An alternative formulation of the control problem as a semidefinite programming problem allows computation of suboptimal solutions. This is illustrated in one example of inertial particles subject to a constant rate killing.
Authors: Yongxin Chen, Tryphon Georgiou, Michele Pavon
Institutions: University of Minnesota, University of Padua
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W2148136046