Optimal Public Sector Support for the High Technology Sector in the Presence of Dynamic Venture Capital Funding

We derive a diffusive stochastic differential equation that describes the dynamics of the venture capital (VC) industry and use it to study two related issues that are concerned with the evolution of the venture capital and the high technology sectors over time. First, the short-term cyclical behavior of the venture capital industry is discussed. Then, we deal with the optimal funding of the public sector for supporting the high technology sector. We address the first issue via a differential equation. For the latter issue, we construct a decision-making model that yields the optimal funding of the public sector for the high technology sector. Our findings indicate that the VC industry is highly correlated with the US capital markets. Hence, the NASDAQ composite stock index can be used for the estimation of the evolution of the venture capital industry with respect to the relevant industry-related variables such as fundraising, the average deal size, the total number of investments and the like. In general, the optimal funding policy of the public sector is shown to be anti-cyclical with the VC funding. Namely, it should be a dynamic funding policy that is conditioned on VC investments and on the specific industrial sector that is supported. For example, the public sector's support for fast maturing sectors like software and information technology should be different than that of slow maturing sectors like pharmaceuticals and biotechnology.