Modelling information flow in stochastic optimal control: How Meyer-$σ$-fields settle the clash between exogenous and endogenous jumps

Peter Bank, David Besslich

Published 2018-10-19Version 1

In stochastic control one seeks to find an intervention policy that optimally controls a stochastic system. Delicate issues arise when the considered system can jump due to both exogenous shocks and endogenous controls. Here one has to specify what the controller knows about the exogenous shocks and how and when she can act on this information. We propose to use Meyer-$\sigma$-fields as a flexible tool to model information flow in such situations. The possibilities of this approach are illustrated first in a very simple linear stochastic control problem and then in a fairly general formulation for the singular stochastic control problem of irreversible investment with inventory risk. For the latter, we illustrate in a first case study how different signals on exogenous jumps lead to different optimal policies, interpolating between the predictable and optional optimal controls in a systematic manner.