Optimal Investment Decision Making Under Two Factor Uncertainty Using L´evy Processes

Abstract

This research presents and examines a problem in which a production company makes investment decisions using the real options approach. The assumption is that investment decisions are based on the dynamics of revenue streams from two different products. The processes are driven by geometric Brownian motion and compensated Poisson random jumps. In this situation, the classical net present value approach has some glaring shortcomings in modelling uncertainty associated with investment decisions, especially in environments characterised by sudden changes in production streams. To address these limitations, this research applies stochastic optimal stopping theory for L\'evy processes to investigate the problem. The main result is a theorem presented as variational inequalities for the optimal stopping problem. Partial integro-differential equations are derived from the valuation problem. An efficient, stable and convergent numerical scheme is deployed to solve the partial integro-differential equation. The results of the research show that infinite jump activities affect investment thresholds. The work also demonstrates the impact of L\'evy markets on the decision process of production firms.