A Maximum Principle for Stochastic Control with Partial Information

Abstract

Abstract. We study the problem of optimal control of a jump diffusion, i.e. a process which is the solution of a stochastic differential equation driven by Lévy processes. It is required that the control process is adapted to a given subfiltration of the filtration generated by the underlying Lévy processes. We prove two maximum principles (one sufficient and one necessary) for this type of partial information control. The results are applied to a partial information mean-variance portfolio selection problem in finance.

A maximum principle for optimal control problem of fully coupled forward-backward stochastic systems with partial information

“…For partial observation stochastic optimal control problem of forward systems, there is already a rich literature and some versions of a corresponding maximum principle have been developed by many authors, see the examples [4][5][6][7] and the references therein. Recently, Baghery and Oksendal [8] established a maximum principle of forward systems for the type of partial information in our paper. In [8], the authors point out that because of the general nature of the partial information filtration {ε t } t 0 , dynamic programming and Hamilton-JacobiBellman equation can not be used to solve the corresponding stochastic optimal control problem.…”

Stochastic Stackelberg equilibria with applications to time-dependent newsvendor models

“…al (2004) and Baghery and Øksendal (2007)) to find a maximum principle for Stackelberg equilibria. To this end, define the Hamiltonian…”

On Mean-Field Partial Information Maximum Principle of Optimal Control for Stochastic Systems with Lévy Processes

“…This kind of problem has potential applications in different fields of economics and finance. Under partial information, the necessary and sufficient conditions of optimality for SDEs with jumps have been proved in [9]. Since the work of Kac [10], the theory of mean-field SDEs has found important applications and has become a powerful tool in many fields, such as mathematical finance, optimal control and stochastic games; see [11].…”