Abstract
Skiba or DNSS sets are an important feature of many deterministic (usually convex or at least non-concave) optimal control models. For stochastic models they have hardly been studied. Using a classical discretization scheme, we consider a time-discrete stochastic reformulation of a well-known optimal control model of illicit drug consumption, in which the retail drug price is influenced by exogenous random forces. We assume that these exogenous forces are described by i.i.d. random variables on a finite probability space. Having set up the model in this way, we use techniques from dynamic programming to determine the optimal solution and describe the transient sets that constitute the stochastic Skiba/DNSS sets. We also show that the DNSS sets expand with the variance, and the optimal policy becomes a continuous function of the state for sufficiently high levels of the variance.
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Bultmann, R., Feichtinger, G., Tragler, G. (2010). Stochastic Skiba Sets: An Example from Models of Illicit Drug Consumption. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2009. Lecture Notes in Computer Science, vol 5910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12535-5_27
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DOI: https://doi.org/10.1007/978-3-642-12535-5_27
Publisher Name: Springer, Berlin, Heidelberg
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