Investment Decisions with Two-Factor Uncertainty

Abstract

This paper considers investment problems in real options with non-homogeneous two-factor uncertainty. We derive some analytical properties of the resulting optimal stopping problem and present a finite difference algorithm to approximate the firm’s value function and optimal exercise boundary. An important message in our paper is that the frequently applied quasi-analytical approach underestimates the impact of uncertainty. This is caused by the fact that the quasi-analytical solution does not satisfy the partial differential equation that governs the value function. As a result, the quasi-analytical approach may wrongly advise to invest in a substantial part of the state space.

A real options analysis of existing green energy facilities: maintain or replace?

“…hitting either p * L from above or p * H from below, given a current price in between the thresholds. 8 We observe that the expected time to exit the inaction region, for the current price p = 50 , first increases in volatility and then decreases. This can be explained by the fact that both the replacement option and compound option become more valuable Fig.…”

“…[28]. Taking the derivative of expression (8) with respect to E gives (57) , gives Differentiating (12) with respect to E gives which is greater than zero for all 𝛽 M > 1 , which shows the second part of the proposition.…”

On an Irreversible Investment Problem with Two-Factor Uncertainty

“…In that work, the authors derived some important preliminary results regarding the value function as well as the corresponding optimal boundary, but did not achieve a complete characterization of the latter. In this work, we push the analysis of Compernolle et al [10] much further. Borrowing arguments from De Angelis et al [11], we determine an integral equation for the optimal investment boundary (cf.…”

“…In this paper, we consider and solve optimal investment problem (1.1), which was first introduced by Compernolle et al [10]. In that work, the authors derived some important preliminary results regarding the value function as well as the corresponding optimal boundary, but did not achieve a complete characterization of the latter.…”

“…To our knowledge, such a result appears here for the first time. As a matter of fact, the analytical approach to comparative statics in Olsen and Stensland [28] (also employed by Compernolle et al [10]) seems to overlook the delicate issue of the regularity of the value function. We are able to fix this issue by providing the proper regularity property, that in turn allows for a rigorous proof of the claimed monotonicity results and for additional findings (cf.…”