We study optimal irreversible investment in a project with infinite horizon when its present value V and its cost I are jump-diffusions. Our analysis accomodates for firm's subjective risk attitude and for her subjective discount rate if the net present value of entering the project cannot be spanned. The properly discounted V is employed as the numeraire. This choice of numeraire transforms the investment problem into a perpetual American put problem, empowering explicit formulae for the investment option value and for the optimal investment policy. We show that natural levels of risk, risk attitude, and discount rate can lead to a non-standard double continuation region: The firm waits to invest if V over I is too low as well as if V over I is too high.
Closed-form optimal investment when present values and costs are jump-diffusions
SBUELZ, Alessandro
2006-01-01
Abstract
We study optimal irreversible investment in a project with infinite horizon when its present value V and its cost I are jump-diffusions. Our analysis accomodates for firm's subjective risk attitude and for her subjective discount rate if the net present value of entering the project cannot be spanned. The properly discounted V is employed as the numeraire. This choice of numeraire transforms the investment problem into a perpetual American put problem, empowering explicit formulae for the investment option value and for the optimal investment policy. We show that natural levels of risk, risk attitude, and discount rate can lead to a non-standard double continuation region: The firm waits to invest if V over I is too low as well as if V over I is too high.
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