This paper analyzes numerically the problem of an entrepreneur who would like to invest in a risky project by taking a loan from a bank. He chooses one from projects with different levels of risk and he has to put efforts to manage the project. We would like to find the optimal level of risk and effort to maximize his utility. Since there is no fully explicit solution, we need to conduct numerical analysis to see how the entrepreneurs’ decisions change according to the initial conditions. This paper explains numerically the relation between the optimal choices, the initial wealth and the time to invest when the utility functions are CRRA utility functions with different coefficients of relative risk aversion. Moreover, this paper also discusses how the parameters affect the optimal solutions and compare the results under different CRRA utility functions.
