A Bayesian Adaptive Singular Control Problem with Discretionary Stopping Arising from Finance

• Activity Number: 520
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Stephane Villeneuve*+
• Companies: Université de Toulouse 1 Capitole
• Keywords: Singular control ; optimal stopping ; Skohorod reflection ; filtering ; finance

Abstract

Stochastic optimization problems that combine features of both bounded variation control and stopping are relatively scarce in the applied probability literature. Recently, mixed stochastic control problems have emerged from corporate finance in continuous time. Bounded variation control problems arise in the corporate finance literature when we consider the optimal liquidity management (dividend and issuance policies) of a firm subject to costly external financing. On the other hand, discretionary stopping in stochastic control arises naturally in solvency risks problems where the shareholders have to determine endogenously the optimal time to liquidate a project. In this paper, we analyse the interaction between dividend policy (the bounded variation control) and optimal abandonment (discretionary stopping) of a liquidity constrained firm whose profitability is partially known. This lead us to study a mixed singular/optimal stopping problem under partial information on the drift of a diffusion that we solve explicitly in some special cases. Moreover, sufficient conditions for the existence of optimal strategies relying on Skohorod reflection are provided.