Discounting Axioms Imply Risk Neutrality
- Matthew Sobel
Annals of Operations Research, 1 ed., vol. 208, pp. 417-432, August 2013
In memory of Professors Cyrus Derman and Robert Rosenthal. Although most applications of discounting occur in risky settings, the best-known axiomatic justifications are deterministic. This paper provides an axiomatic rationale for discounting in a stochastic framework. Consider a binary relation on a real vector space of vector-valued discrete-time stochastic processes on a probability space. Four axioms imply that there are unique discount factors such that preferences among stochastic processes correspond to preferences among present value random vectors. The familiar axioms are weak ordering, continuity and nontriviality. The fourth axiom, decomposition, is non-standard and key. These axioms and the converse of decomposition are assumed in previous axiomatic justifications for discounting with nonlinear intraperiod utility functions in deterministic frameworks. Thus, the results here provide the weakest known sufficient conditions for discounting in deterministic or stochastic settings. In addition to the four axioms, if there exists a von Neumann-Morgenstern utility function, then that function is affine. In this sense, discounting axioms imply risk neutrality.