Proactive and Reactive Investments via Meyer-σ-fields

Stochastic control problems search optimal strategies given some information flow. Imagine a moment information is known to become available. Controller will make a precautionary action right before and a reaction right... [ view full abstract ]

Stochastic control problems search optimal strategies given some information flow. Imagine a moment information is known to become available. Controller will make a precautionary action right before and a reaction right afterwards depending on the own expectations. This suggests neither predictable nor merely adapted controls. We use Meyer-σ-fields to capture this and apply it in an irreversible investment problem with inventory risk, where we construct optimal policies in a Lévy process setting, which depend on a generalized version of a representation problem of Bank & El Karoui (2004). For this extension we used the théorie générale des processus stochastiques.