New Stochastic Orders and Monotone Comparative Statics of Changes in Risk under Risk Aversion

Abstract

We define two new stochastic orders combining probability ratio and likelihood ratio and specify two respective classes of payoff functions, which nest most models in the literature as special cases, such that a risk change satisfies one of the two stochastic orders if and only if given any payoff function in the corresponding class, it always has a monotone effect on any risk averse agent's decision variable. We then apply the two stochastic orders to some classic decision problems in economics and finance including a portfolio problem, two insurance problems, and four management decision problems and present a simple sufficient condition for monotone comparative statics of changes in risk under risk aversion.

Keywords: comparative statics, changes in risk, risk aversion, central dominance, probability ratio, likelihood ratio, portfolio decisions, insurance decisions, management decisions

JEL Classification: D81, G11