An Optimal Rule for Switching over to Renewable fuels with Lower Price Volatility: A Case of Jump Diffusion Process

This study investigates the optimal switching boundary to a renewable fuel when oil prices exhibit continuous random fluctuations along with occasional discontinuous jumps. In this paper, oil prices are modeled to follow jump diffusion processes. A completeness result is derived. Given that the market is complete the value of a contingent claim is risk neutral expectation of the discounted pay off process. Using the contingent claim analysis of investment under uncertainty, the Hamilton-Jacobi-Bellman (HJB) equation is derived for finding value function and optimal switching boundary. We get a mixed differential-difference equation which would be solved using numerical methods.