A Mathematical Model for the Role of Third Party Funding in Reputation Building of Academic Institutions

Abstract

[Abstract] Previous research on third party funding for academic institutions has demonstrated that it entails positive and negative outcomes. This manuscript deals with this idea from a reputational perspective, using the options theory as the framework for the analysis. The reasoning is based on the definition of a reputational income that is supposed to follow a stochastic behavior. It is modelled as a mean reverting type process, which is modified to introduce a correction factor with the aim of capturing the special reputational sensitivity of academic institutions regarding funding issues. We develop a stochastic partial differential equation, and we use its solution to deploy a sensitivity analysis to identify how the value of reputation reacts to changes in certain key variables. We find that the value of reputation increases if the academic institution becomes more sensitive to reputation related issues, or if there is an increase in the reputational reward that the market offers to a continued commitment to third-party funding. Also, the value of reputation gets higher as the ability to recover from reputational pitfalls strengths, but it decreases in a framework with high uncertainty and risk. So, this research proposes a mathematical formalization for the reputational dimension of third party funding in academic institutions, with the aim of identifying the critical variables that are likely to affect their reputational value and, thus, assist managers in their decision-making processes.