A Singular Stochastic Control Problem with Interconnected Dynamics

Federico S, Ferrari G, Schuhmann P (2020)
SIAM Journal on Control and Optimization 58(5): 2821-2853.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
In this paper we study a Markovian two-dimensional bounded-variation stochastic control problem whose state process consists of a diffusive mean-reverting component and of a purely controlled one. The main problem's characteristic lies in the interaction of the two components of the state process: the mean-reversion level of the diffusive component is an affine function of the current value of the purely controlled one. By relying on a combination of techniques from viscosity theory and free-boundary analysis, we provide the structure of the value function and we show that it satisfies a second-order smooth-fit principle. Such a regularity is then exploited in order to determine a system of functional equations solved by the two monotone continuous curves (free boundaries) that split the control problem's state space into three connected regions. Further properties of the free boundaries are also obtained.
Stichworte
singular stochastic control; Dynkin game; viscosity solution; free; boundary; smooth-fit; inflation management
Erscheinungsjahr
2020
Zeitschriftentitel
SIAM Journal on Control and Optimization
Band
58
Ausgabe
5
Seite(n)
2821-2853
ISSN
0363-0129
eISSN
1095-7138
Page URI
https://pub.uni-bielefeld.de/record/2949212

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Federico S, Ferrari G, Schuhmann P. A Singular Stochastic Control Problem with Interconnected Dynamics . SIAM Journal on Control and Optimization. 2020;58(5):2821-2853.
Federico, S., Ferrari, G., & Schuhmann, P. (2020). A Singular Stochastic Control Problem with Interconnected Dynamics . SIAM Journal on Control and Optimization, 58(5), 2821-2853. doi:10.1137/19M1296288
Federico, S., Ferrari, G., and Schuhmann, P. (2020). A Singular Stochastic Control Problem with Interconnected Dynamics . SIAM Journal on Control and Optimization 58, 2821-2853.
Federico, S., Ferrari, G., & Schuhmann, P., 2020. A Singular Stochastic Control Problem with Interconnected Dynamics . SIAM Journal on Control and Optimization, 58(5), p 2821-2853.
S. Federico, G. Ferrari, and P. Schuhmann, “A Singular Stochastic Control Problem with Interconnected Dynamics ”, SIAM Journal on Control and Optimization, vol. 58, 2020, pp. 2821-2853.
Federico, S., Ferrari, G., Schuhmann, P.: A Singular Stochastic Control Problem with Interconnected Dynamics . SIAM Journal on Control and Optimization. 58, 2821-2853 (2020).
Federico, Salvatore, Ferrari, Giorgio, and Schuhmann, Patrick. “A Singular Stochastic Control Problem with Interconnected Dynamics ”. SIAM Journal on Control and Optimization 58.5 (2020): 2821-2853.

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