Mathematical Methods of Operations Research

, Volume 67, Issue 1, pp 21–42

Optimizing venture capital investments in a jump diffusion model

Original Article

Abstract

We study two practical optimization problems in relation to venture capital investments and/or Research and Development (R&D) investments. In the first problem, given the amount of the initial investment and the cash flow structure at the initial public offering (IPO), the venture capitalist wants to maximize overall discounted cash flows after subtracting subsequent investments, which keep the invested company solvent. We describe this problem as a mixture of singular stochastic control and optimal stopping problems. The second problem is concerned with optimal dividend policy. Rather than selling the company at an IPO, the investor may want to harvest technological achievements in the form of dividend when it is appropriate. The optimal control policy in this problem is a mixture of singular and impulse controls.

Keywords

Venture capital investments R&D IPO Stochastic control Optimal stopping Singular control Impulse control Jump diffusions 

Mathematics Subject Classification (2000)

Primary 49N25 Secondary 60G40 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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