Optimizing venture capital investments in a jump diffusion model
- First Online:
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.
KeywordsVenture capital investments R&D IPO Stochastic control Optimal stopping Singular control Impulse control Jump diffusions
Mathematics Subject Classification (2000)Primary 49N25 Secondary 60G40
Unable to display preview. Download preview PDF.
- Bayraktar E, Egami M (2006) A unified treatment of dividend payment problems under fixed cost and implementation delay (Submitted), http://arxiv.org/abs/math.OC/0703825
- Davis M, Schachermayer W and Tompkins R (2004). The evaluation of venture capital as an instalment option. Zeitschrift für Betriebswirtschaft 3: 77–96 Google Scholar
- Gerber HU (1968). Entscheidungskriterien fuer den zusammengesetzten poisson-prozess. Schweiz Aktuarver Mitt 1: 185–227 Google Scholar
- Grandits P, Hubalek F, Schachermayer W, Zigo M (2007) Optimal expected exponential utility of dividend payments in brownian risk model. Scand Actuar J (in press), http://www.fam.tuwien.ac.at/~wschach/pubs
- Jacod J and Shiryaev A (1987). Limit theorem for stochastic processes. Springer, Berlin Google Scholar
- Øksendal B and Sulem A (2005). Applied stochastic controll of jump diffusions. Springer, New York Google Scholar
- Schmidli H (2007). Optimal control in insurance. Springer, New York Google Scholar
- Willner R (1995). Valuing start-up venture growth options in real options in capital investments. MIT, Cambridge Google Scholar