Taxation under Uncertainty – Problems of Dynamic Programming and Contingent Claims Analysis in Real Option Theory

This article deals with the integration of taxes into real option-based investment models under risk neutrality and risk averison. It compares the possible approaches dynamic programming and contingent claims analysis to analyze their effects on the optimal investment rules before and after taxes. It can be shown that despite their different assumptions, dynamic programming and contingent claims analysis yield identical investment thresholds under risk neutrality. In contrast, under risk aversion, there are severe problems in determining an adequate risk-adjusted discount rate. The application of contingent claims analysis is restricted to cases with a dividend rate unaffected by risk. Therefore, only dynamic programming permits an explicit investment threshold without taxation. After taxes, both approaches fail to reach general solutions. Nevertheless, using a sufficient condition, it is possible to derive neutral tax systems under risk aversion as is demonstrated by using dynamic programming.