Open Access
December 2013 A control problem with fuel constraint and Dawson–Watanabe superprocesses
Alexander Schied
Ann. Appl. Probab. 23(6): 2472-2499 (December 2013). DOI: 10.1214/12-AAP908


We solve a class of control problems with fuel constraint by means of the log-Laplace transforms of $J$-functionals of Dawson–Watanabe superprocesses. This solution is related to the superprocess solution of quasilinear parabolic PDEs with singular terminal condition. For the probabilistic verification proof, we develop sharp bounds on the blow-up behavior of log-Laplace functionals of $J$-functionals, which might be of independent interest.


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Alexander Schied. "A control problem with fuel constraint and Dawson–Watanabe superprocesses." Ann. Appl. Probab. 23 (6) 2472 - 2499, December 2013.


Published: December 2013
First available in Project Euclid: 22 October 2013

zbMATH: 1288.60100
MathSciNet: MR3127942
Digital Object Identifier: 10.1214/12-AAP908

Primary: 60J80 , 60J85 , 93E20
Secondary: 60H20 , 60H30 , 91G80

Keywords: $J$-functional , Dawson–Watanabe superprocess , Log-Laplace equation , optimal stochastic control with fuel constraint , optimal trade execution

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.23 • No. 6 • December 2013
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