# Learning and risk aversion

## Abstract

This dissertation contains three essays on learning and risk aversion. In the first essay we consider how learning may lead to risk averse behavior. A learning rule is said to be risk averse if it is expected to add more probability to an action which provides, with certainty, the expected value of a distribution rather than when it provides a randomly drawn payoff from this distribution, for every distribution. We characterize risk averse learning rules. The result reveals that the analysis of risk averse learning is isomorphic to that of risk averse expected utility maximizers. A learning rule is said to be monotonically risk averse if it is expected to increase the probability of choosing the actions whose distribution second-order stochastically dominates all others in every environment. We characterize monotonically risk averse learning rules. In the second essay we analyze risk attitudes for learning within the mean-variance paradigm. A learning rule is variance-averse if the expected reduced distribution of payoffs in the next period has a smaller variance than that of the current reduced distribution, in every set where all the actions provide the same expected payoff. A learning rule is monotonically variance-averse if it is expected to add probability to the set of actions that have the smallest variance in the set, when all the actions have the same expected payoff. A learning rule is monotonically mean-variance-averse if it is expected to add probability to the set of actions that have the highest expected payoff and smallest variance whenever this set is not empty. We characterize monotonically variance-averse and monotonically mean-variance-averse learning rules. In the last essay we analyze the social learning process of a group of individuals. We say that a learning rule is first-order monotone if the number of individuals that play actions with first-order stochastic dominant payoff distributions is expected to increase. We characterize these learning rules.