On an integral equation for the free-boundary of stochastic, irreversible investment problems

Ferrari G (2015)
The Annals of Applied Probability 25(1): 150-176.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
In this paper, we derive a new handy integral equation for the freeboundary of infinite time horizon, continuous time, stochastic, irreversible investment problems with uncertainty modeled as a one-dimensional, regular diffusion X. The new integral equation allows to explicitly find the freeboundary b(.) in some so far unsolved cases, as when the operating profit function is not multiplicatively separable and X is a three-dimensional Bessel process or a CEV process. Our result follows from purely probabilistic arguments. Indeed, we first show that b(X (t)) = l* (t), with l* the unique optional solution of a representation problem in the spirit of Bank El Karoui [Ann. Probab. 32 (2004) 1030-1067]; then, thanks to such an identification and the fact that l* uniquely solves a backward stochastic equation, we find the integral problem for the free-boundary.
Stichworte
and El Karoui's representation theorem; one-dimensional diffusion; Bank; optimal stopping; stochastic control; singular; irreversible investment; free-boundary; Integral equation; base capacity
Erscheinungsjahr
2015
Zeitschriftentitel
The Annals of Applied Probability
Band
25
Ausgabe
1
Seite(n)
150-176
ISSN
1050-5164
Page URI
https://pub.uni-bielefeld.de/record/2718995

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Ferrari G. On an integral equation for the free-boundary of stochastic, irreversible investment problems. The Annals of Applied Probability. 2015;25(1):150-176.
Ferrari, G. (2015). On an integral equation for the free-boundary of stochastic, irreversible investment problems. The Annals of Applied Probability, 25(1), 150-176. doi:10.1214/13-AAP991
Ferrari, G. (2015). On an integral equation for the free-boundary of stochastic, irreversible investment problems. The Annals of Applied Probability 25, 150-176.
Ferrari, G., 2015. On an integral equation for the free-boundary of stochastic, irreversible investment problems. The Annals of Applied Probability, 25(1), p 150-176.
G. Ferrari, “On an integral equation for the free-boundary of stochastic, irreversible investment problems”, The Annals of Applied Probability, vol. 25, 2015, pp. 150-176.
Ferrari, G.: On an integral equation for the free-boundary of stochastic, irreversible investment problems. The Annals of Applied Probability. 25, 150-176 (2015).
Ferrari, Giorgio. “On an integral equation for the free-boundary of stochastic, irreversible investment problems”. The Annals of Applied Probability 25.1 (2015): 150-176.