Closed-Form Optimal Investment when Present Values and Costs are Jump-Diffusions

26 Pages Posted: 6 Mar 2007

See all articles by Alessandro Sbuelz

Alessandro Sbuelz

Catholic University of Milan - Department of Mathematics, Quantitative Finance, and Econometrics; Bocconi University - CAREFIN - Centre for Applied Research in Finance

Anna Battauz

Bocconi University - Department of Finance

Date Written: November 2006

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. The result does not depend on the presence of jumps.

Keywords: Investment under uncertainty, optimal stopping, change of numeraire, perpetual American put, double continuation region

Suggested Citation

Sbuelz, Alessandro and Battauz, Anna, Closed-Form Optimal Investment when Present Values and Costs are Jump-Diffusions (November 2006). Available at SSRN: https://ssrn.com/abstract=968172 or http://dx.doi.org/10.2139/ssrn.968172

Alessandro Sbuelz (Contact Author)

Catholic University of Milan - Department of Mathematics, Quantitative Finance, and Econometrics ( email )

largo A. Gemelli 1
I-20123 Milan
Italy
+39 02 7234 2345 (Phone)
+39 02 7234 2671 (Fax)

HOME PAGE: http://ppd.unicatt.it/docenti/alessandro_sbuelz

Bocconi University - CAREFIN - Centre for Applied Research in Finance

Via Sarfatti, 25
Milan, 20136
Italy

Anna Battauz

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

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