An Integral Equation Approach to the Irreversible Investment Problem with a Finite Horizon

This paper studies an irreversible investment problem under a finite horizon. The firm expands its production capacity in irreversible investments by purchasing capital to increase productivity. This problem is a singular stochastic control problem and its associated Hamilton–Jacobi–Bellman equation is derived. By using a Mellin transform, we obtain the integral equation satisfied by the free boundary of this investment problem. Furthermore, we solve the integral equation numerically using the recursive integration method and present the graph for the free boundary.

Valuation of Logistics Hubs

Logistics structures playing significant roles in the economic development of countries are irreversible investments. The exact valuation of them could be difficult due to various uncertainties and problems. This chapter illustrates a methodological way to be able to make an investment decision about the creation of a logistics hub in Of-Iyidere region. Under given assumptions, the study findings indicate that (1) the investment has a positive net present value under three different cost of capital rates, which are 7.5%, 10%, and 15%; (2) the internal rate of return is 18.5%; (3) the payback period is 7 years 8 months; and (4) the discounted payback periods are calculated as 10 years 1 month, 11 years 3 months, and 14 years 11 months according to the aforementioned cost of capital rates. Moreover, the chapter discusses basic project valuation challenges and presents solutions to improve the practice of logistics hub appraisal. So, the paper exhibits an essential guidance and policy support tool to highlight the potential of logistics hub infrastructures in Turkey.

Asymmetric Effects on Fatality Rates of Changes in Workers’ Compensation Laws

With irreversible investments in safety, changes in workers’ compensation laws should affect employer incentives asymmetrically: increases in workers’ compensation generosity should cause employers to invest more in safety, but comparable decreases might not cause them to disinvest in existing precautionary programs or equipment. Although maximum weekly benefits caps have been fairly stable, state laws have expanded or restricted workers’ compensation on multiple other dimensions. State laws may impose new requirements regarding burdens of proof, access to medical care, and the duration of benefits. This article estimates the effect of changes in these more comprehensive measures of workers’ compensation laws on workplace safety. Using confidential, restricted data from the Census of Fatal Occupational Injuries, the article finds that increases in workers’ compensation generosity lead to a significant decrease in fatality rates, while decreases in workers’ compensation generosity do not significantly increase fatality rates.

IRREVERSIBLE INVESTMENTS AND AMBIGUITY AVERSION

Real option valuation has traditionally been concerned with investment under project value uncertainty while assuming that the agent has perfect confidence in a specific model. However, agents do not generally have perfect confidence in their model and this ambiguity may affect their decisions. In addition, the value of real investments is not typically fully spanned by tradable assets because markets are incomplete as is typically the case in energy and commodities. In this paper, we account for the agent’s aversion to model ambiguity and address market incompleteness through the notion of robust indifference prices. We derive analytical results for the perpetual option to invest and the linear complementarity problem that the finite-time version of this problem satisfies. Ambiguity aversion has a number of effects on decision making some of which cannot be explained by altering the agent’s risk aversion. For example, ambiguity averse agents are found to exercise real options both earlier and later than their ambiguity neutral counterparts, depending on whether ambiguity stems from uncertainty in the dynamics of the project value or the dynamics of a hedging asset.

Dynamic Free Riding with Irreversible Investments

We study the Markov equilibria of a model of free riding in which n infinitely lived agents choose between private consumption and irreversible contributions to a durable public good. We show that the set of equilibrium steady states converges to a unique point as depreciation converges to zero. For any level of depreciation, moreover, the highest steady state converges to the efficient level as agents become increasingly patient. These results are in contrast to the case with reversible investments, where a continuum of inefficient equilibrium steady states exists for any level of depreciation, discount factor, and size of population. (JEL D11, H41)