The myopic property in decision models

摘要

The optimal decision in decision analysis is obtained by considering the impact of the current decision on all future decisions. This is done using a grand decision tree that models decisions and uncertainties in all periods. It may be difficult for a decision maker to deal with a grand model, and instead would like to take it up as small problems in isolation. Such a method is likely to produce a suboptimal solution. This article considers decision situations and utility functions for which solving a sequence of problems generate globally optimum solutions. In these cases, only a few observations will be available to examine for the optimum decision. The shifting in future information has no impact on the present decision. Even in two-period decisions, full decision trees are not constructed and all future contingencies are not considered. Investment decisions have the uncertainty with constant returns to scale. The return on investment is known at the end of the investment period. An investor divides his wealth into two parts. The first part he keeps for consumption and sustenance and the second he uses for investments. This part is called initial capital and is invested based on the expected utility of the final capital bounded by the initial wealth. The baseline decision model is subjective expected utility. That allows for myopic decision rule probabilities that are either given or subjectively determined. The utility function allow myopic decision rules to focus on the current period, while choosing optimality with respect to the multi-period model. The objective of this study is not only to find some utility functions that possess myopic properties, but to identify all such functions. The first contribution of this study is that no assumption of the form of the VNM utility (Ref. 1) is made except for monotonicity and differentiability and the log utility over capital is serially correlated. The second contribution is that the study shows that power and log utility over capital are the only forms that possess the myopic property. The study focuses on the KMM smooth recursive model of ambiguity by Klibanoff et al. (Ref. 2) as it offers the most promise for the myopic property. This model applies a prior-by-prior Bayesian updating and allows for backward induction and dynamic consistency. The third contribution is to fill the gap in the literature about the properties of serially correlated returns.