Optimality of doubly reflected Lévy processes in singular control

Baurdoux, Erik J. and Yamazaki, Kazutoshi (2015) Optimality of doubly reflected Lévy processes in singular control. Stochastic Processes and Their Applications, 125 (7). pp. 2727-2751. ISSN 0304-4149

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Abstract

We consider a class of two-sided singular control problems. A controller either increases or decreases a given spectrally negative Lévy process so as to minimize the total costs comprising of the running and controlling costs where the latter is proportional to the size of control. We provide a sufficient condition for the optimality of a double barrier strategy, and in particular show that it holds when the running cost function is convex. Using the fluctuation theory of doubly reflected Lévy processes, we express concisely the optimal strategy as well as the value function using the scale function. Numerical examples are provided to confirm the analytical results.

Item Type:	Article
Official URL:	http://www.sciencedirect.com/science/journal/03044...
Additional Information:	© 2015 Elsevier
Library of Congress subject classification:	H Social Sciences > HA Statistics
Sets:	Departments > Statistics
Funders:	MEXT KAKENHI, JSPS KAKENHI, Inamori foundation research grant, Kansai University subsidy for supporting young scholars
Projects:	22710143 , 26800092, 23310103
Date Deposited:	16 Apr 2015 13:58
URL:	http://eprints.lse.ac.uk/61617/

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