A Maximum Principle for Stochastic Control with Partial Information

Fouzia Baghéry · Bernt Øksendal

110 citations0/0 files storedStochastic Analysis and Applications

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Stochastic processes and financial applications Risk and Portfolio Optimization Probability and Risk Models

Abstract

We study the problem of optimal control of a jump diffusion, that is, 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.

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References

2005Applied Stochastic Control of Jump Diffusions 2007Applied Stochastic Control of Jump Diffusions 1983Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions 1998The Maximum Principle for Partially Observed Optimal Control of Stochastic Differential Equations 2004Sufficient Stochastic Maximum Principle for the Optimal Control of Jump Diffusions and Applications to Finance

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2013Stochastic Stackelberg equilibria with applications to time-dependent newsvendor models 2008Maximum Principle for Stochastic Differential Games with Partial Information 2010Maximum Principle for Partially-Observed Optimal Control of Fully-Coupled Forward-Backward Stochastic Systems 2017Linear-quadratic stochastic Stackelberg differential game with asymmetric information 2009A maximum principle for optimal control problem of fully coupled forward-backward stochastic systems with partial information 2008Partial Information Linear Quadratic Control for Jump Diffusions 2013Maximum principles for jump diffusion processes with infinite horizon

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