Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/22720 
Autor:innen: 
Erscheinungsjahr: 
2005
Schriftenreihe/Nr.: 
Dresden Discussion Paper Series in Economics No. 03/05
Verlag: 
Technische Universität Dresden, Fakultät Wirtschaftswissenschaften, Dresden
Zusammenfassung: 
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.
Schlagwörter: 
Stochastic differential equation
Poisson process
Bellman equation
JEL: 
C61
Dokumentart: 
Working Paper

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