Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7374569 | Physica A: Statistical Mechanics and its Applications | 2018 | 16 Pages |
Abstract
The purpose of this paper is to design an optimal quantum controller for a class of stochastic systems with application in financial problems. Dynamics of the system is prescribed via a Quantum Stochastic Differential System (QSDES) with a quantum Brownian motion on a quantum probability space. A theorem for guaranteeing the existence and uniqueness of solutions to the QSDES is proved. Additionally, a new optimal stochastic control problem is formulated and based on the necessary optimality conditions, an optimal quantum control law is designed, explicitly. Four theorems and two lemmas, for facilitating the optimal controller design algorithm, are proved. Finally, for demonstrating the applicable results, two financial problems, Merton portfolio allocation and optimal pairs trading problem are simulated by using the presented method. As the simulation results indicate, portfolio optimal performances, minimum risk and maximum return, are achieved via presented method.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
S. Yaghobipour, M. Yarahmadi,