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We study a practical optimization problems for venture capital investmentsand/or Research and Development (R&D) investments. The first problem is that,given the amount of the initial investment and the reward function at theinitial public offering (IPO) market, the venture capitalist wants to maximizeoverall discounted cash flows after subtracting subsequent (if needed)investments. We describe this problem as a mixture of singular stochasticcontrol and optimal stopping problems and give an explicit solution. The formercorresponds to finding an optimal subsequent investment policy for the purposethat the value of the investee company stays away from zero. The lattercorresponds to finding an optimal stopping rule in order to maximize theharvest of their investments. The second kind problem is concerned aboutoptimal dividend policy. Rather than selling the holding stock, the investormay extract dividends when it is appropriate. We will find a quasi-explicitoptimal solution to this problem and prove the existence and uniqueness of thesolution and the optimality of the proposed strategy.

Optimizing venture capital investments in a jump diffusion model