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

Ferrari G (2012) Working Papers. Institute of Mathematical Economics; 471.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
In this paper we derive a new handy integral equation for the free boundary of infinite time horizon, continuous time, stochastic, irreversible investment problems with uncertainty modeled as a one-dimensional, regular diffusion X0;x. The new integral equation allows to explicitly find the free boundary b(.) in some so far unsolved cases, as when X0;x is a three-dimensional Bessel process or a CEV process. Our result follows from purely probabilistic arguments. Indeed, we first show that b(X0;x(t)) = l*(t), with l*(t) unique optional solution of a representation problem in the spirit of Bank-El Karoui [4]; then, thanks to such identification and the fact that l* uniquely solves a backward stochastic equation, we find the integral problem for the free boundary.
Stichworte
free boundary; irreversible investment; integral equation; singular stochastic control; Bank and El Karoui's Representation Theorem; one-dimensional di usion; optimal stopping; base capacity.
Erscheinungsjahr
2012
Band
471
Seite(n)
20
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2674034

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Ferrari G. On an integral equation for the free boundary of stochastic, irreversible investment problems. Working Papers. Institute of Mathematical Economics. Vol 471. Bielefeld: Center for Mathematical Economics; 2012.
Ferrari, G. (2012). On an integral equation for the free boundary of stochastic, irreversible investment problems (Working Papers. Institute of Mathematical Economics, 471). Bielefeld: Center for Mathematical Economics.
Ferrari, G. (2012). On an integral equation for the free boundary of stochastic, irreversible investment problems. Working Papers. Institute of Mathematical Economics, 471, Bielefeld: Center for Mathematical Economics.
Ferrari, G., 2012. On an integral equation for the free boundary of stochastic, irreversible investment problems, Working Papers. Institute of Mathematical Economics, no.471, Bielefeld: Center for Mathematical Economics.
G. Ferrari, On an integral equation for the free boundary of stochastic, irreversible investment problems, Working Papers. Institute of Mathematical Economics, vol. 471, Bielefeld: Center for Mathematical Economics, 2012.
Ferrari, G.: On an integral equation for the free boundary of stochastic, irreversible investment problems. Working Papers. Institute of Mathematical Economics, 471. Center for Mathematical Economics, Bielefeld (2012).
Ferrari, Giorgio. On an integral equation for the free boundary of stochastic, irreversible investment problems. Bielefeld: Center for Mathematical Economics, 2012. Working Papers. Institute of Mathematical Economics. 471.
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2019-09-06T09:18:23Z
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