Diversification Preferences in the Theory of Choice

Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This corresponds to the notion of risk aversion when one assumes the von-Neumann-Morgenstern expected utility model, but the equivalence fails to hold in other models. This paper studies axiomatizations of the concept of diversification and their relationship to the related notions of risk aversion and convex preferences within different choice theoretic models. Implications of these notions on portfolio choice are discussed. We cover model-independent diversification preferences, preferences within models of choice under risk, including expected utility theory and the more general rank-dependent expected utility theory, as well as models of choice under uncertainty axiomatized via Choquet expected utility theory. Remarks on interpretations of diversification preferences within models of behavioral choice are given in the conclusion

Portfolio Choices and Asset Prices: The Comparative Statics of Ambiguity Aversion

We investigate the comparative statics of "more ambiguity aversion" as defined by Klibanoff, Marinacci and Mukerji (2005) in the context of the static two-asset portfolio problem. It is not true in general that more ambiguity aversion reduces the demand for the uncertain asset. We exhibit some sufficient conditions to guarantee that, ceteris paribus, an increase in ambiguity aversion reduces the demand for the ambiguous asset, and raises the equity premium. For example, this is the case when the set of plausible distributions of returns can be ranked according to the monotone likelihood ratio order. We also show how ambiguity aversion distorts the price kernel in the alternative portfolio problem with complete markets for contingent claims.

A smooth model of decision making under ambiguity.

We propose and axiomatize a new model of preferences that achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective information, and ambiguity attitude, a characteristic of the decision maker's tastes.Ambiguity; Uncertainty; Knightian Uncertainty; Ambiguity Aversion; Uncertainty Aversion; Ellsberg Paradox

A Satisficing Alternative to Prospect Theory

In this paper, we axiomatize a target-based model of choice that allows decision makers to be both risk averse and risk seeking, depending on the payoff's position relative to a prespecified target. The approach can be viewed as a hybrid model, capturing in spirit two celebrated ideas: first, the satisficing concept of Simon (1955); second, the switch between risk aversion and risk seeking popularized by the prospect theory of Kahneman and Tversky (1979). Our axioms are simple and intuitive; in order to be implemented in practice, our approach requires only the specification of an aspiration level. We show that this approach is dual to a known approach using risk measures, thereby allowing us to connect to existing theory. Though our approach is intended to be normative, we also show that it resolves the classical examples of Allais (1953) and Ellsberg (1961).satisficing; aspiration levels; targets; prospect theory; reflection effect; risk measures; coherent risk measures; convex risk measures; portfolio optimization

Robust Optimal Risk Sharing and Risk Premia in Expanding Pools

We consider the problem of optimal risk sharing in a pool of cooperative agents. We analyze the asymptotic behavior of the certainty equivalents and risk premia associated with the Pareto optimal risk sharing contract as the pool expands. We first study this problem under expected utility preferences with an objectively or subjectively given probabilistic model. Next, we develop a robust approach by explicitly taking uncertainty about the probabilistic model (ambiguity) into account. The resulting robust certainty equivalents and risk premia compound risk and ambiguity aversion. We provide explicit results on their limits and rates of convergence, induced by Pareto optimal risk sharing in expanding pools

Horizon-unbiased Investment with Ambiguity

In the presence of ambiguity on the driving force of market randomness, we consider the dynamic portfolio choice without any predetermined investment horizon. The investment criteria is formulated as a robust forward performance process, reflecting an investor's dynamic preference. We show that the market risk premium and the utility risk premium jointly determine the investors' trading direction and the worst-case scenarios of the risky asset's mean return and volatility. The closed-form formulas for the optimal investment strategies are given in the special settings of the CRRA preference