On a class of singular stochastic control problems for reflected diffusions

Ferrari G (2019)
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 473(2): 952-979.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Abstract / Bemerkung
Reflected diffusions naturally arise in many problems from applications ranging from economics and mathematical biology to queueing theory. In this paper, we consider a class of infinite time-horizon singular stochastic control problems for a general one-dimensional diffusion that is reflected at zero. We assume that exerting control leads to a state-dependent instantaneous reward, whereas reflecting the diffusion at zero gives rise to a proportional cost with constant marginal value. The aim is to maximize the total expected reward, minus the total expected cost of reflection. We show that depending on the properties of the state-dependent instantaneous reward we can have qualitatively different kinds of optimal strategies. The techniques employed are those of stochastic control and of the theory of linear diffusions. (C) 2019 Elsevier Inc. All rights reserved.
Erscheinungsjahr
2019
Zeitschriftentitel
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Band
473
Ausgabe
2
Seite(n)
952-979
ISSN
0022-247X
eISSN
1096-0813
Page URI
https://pub.uni-bielefeld.de/record/2934107

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Ferrari G. On a class of singular stochastic control problems for reflected diffusions. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 2019;473(2):952-979.
Ferrari, G. (2019). On a class of singular stochastic control problems for reflected diffusions. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 473(2), 952-979. doi:10.1016/j.jmaa.2019.01.004
Ferrari, G. (2019). On a class of singular stochastic control problems for reflected diffusions. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 473, 952-979.
Ferrari, G., 2019. On a class of singular stochastic control problems for reflected diffusions. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 473(2), p 952-979.
G. Ferrari, “On a class of singular stochastic control problems for reflected diffusions”, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 473, 2019, pp. 952-979.
Ferrari, G.: On a class of singular stochastic control problems for reflected diffusions. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 473, 952-979 (2019).
Ferrari, Giorgio. “On a class of singular stochastic control problems for reflected diffusions”. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 473.2 (2019): 952-979.