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dc.contributor.authorSennewald, Kenen_US
dc.description.abstractThe 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.en_US
dc.relation.ispartofseriesDresden discussion paper in economics 03/05en_US
dc.subject.keywordStochastic differential equationen_US
dc.subject.keywordPoisson processen_US
dc.subject.keywordBellman equationen_US
dc.subject.stwStochastischer Prozessen_US
dc.titleControlled Stochastic Differential Equations under Poisson Uncertainty and with Unbounded Utilityen_US
dc.typeWorking Paperen_US
Appears in Collections:Dresden Discussion Paper Series in Economics, Faculty of Business and Economics, TU Dresden

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