Modelling information flows by Meyer-$\sigma$-fields in the singular stochastic control problem of irreversible investment

TL;DR

This paper introduces Meyer-$\sigma$-fields as a versatile framework to model information flow in complex stochastic control problems involving jumps, with applications to irreversible investment and inventory risk.

Contribution

It develops a novel approach using Meyer-$\sigma$-fields to handle information flow in stochastic control, bridging predictable and optional information scenarios.

Findings

Different signals on exogenous jumps influence optimal controls.

The approach interpolates systematically between predictable and optional cases.

Application to irreversible investment demonstrates practical utility.

Abstract

In stochastic control problems delicate issues arise when the controlled system can jump due to both exogenous shocks and endogenous controls. Here one has to specify what the controller knows when 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 controls, interpolating between the predictable and the optional case in a systematic manner.