Controlled Stochastic Differential Equations under Poisson Uncertainty and with Unbounded Utility

Arbeitspapier

The present paper is concerned with the optimal control of stochastic differential equations, where uncertainty stems from one or more independent Poisson processes. Optimal behavior in such a setup (e.g., optimal consumption) is usually determined by employing the Hamilton-Jacobi-Bellman equation. This, however, requires strong assumptions on the model, such as a bounded utility function and bounded coefficients in the controlled differential equation. The present paper relaxes these assumptions. We show that one can still use the Hamilton-Jacobi-Bellman equation as a necessary criterion for optimality if the utility function and the coefficients are linearly bounded. We also derive sufficiency in a verification theorem without imposing any boundedness condition at all. It is finally shown that, under very mild assumptions, an optimal Markov control is optimal even within the class of general controls.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Dresden Discussion Paper Series in Economics ; No. 03/05

Classification and Topics

• Classification: Wirtschaft ; Optimization Techniques; Programming Models; Dynamic Analysis
• Subject: Stochastic differential equation ; Poisson process ; Bellman equation ; Kontrolltheorie ; Analysis ; Stochastischer Prozess ; Zeitpräferenz ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Sennewald, Ken
• Event: Veröffentlichung
• (who): Technische Universität Dresden, Fakultät Wirtschaftswissenschaften
• (where): Dresden
• (when): 2005

Further information

• Handle: http://hdl.handle.net/10419/22720
• Last update: 10.03.2025, 11:41 AM CET