Discount Factors Ex Post and Ex Ante, and Discounted Utility Anomalies

The real options approach is used to explain discounted utility anomalies as artifacts of the optimizing behavior of an individual with standard preferences, who perceives the utility from consumption in the future as uncertain. For this individual, waiting is valuable because uncertainty is revealed over time. The fair price (or compensation) that the individual agrees to pay (or accept) today is the expected value of utility of the future gain (or loss) multiplied by a certain non-exponential factor which we interpret as a discount factor ex ante. The factors ex ante are different for gains and losses, and depend on the utility function and underlying uncertainty. After the decision of exchange had been made, valuation ex post reduces to calculation of the standard expected present value. We provide analytic expressions and numerical examples for discount factors assuming different utility functions and models of uncertainty, and demonstrate that our explanation of discounted utility anomalies is robust.