Portfolio Choice and Asset Prices in an Economy Populated by Case-Based Decision Makers

I consider an economy populated by case-based decision makers. Consumption can be transferred between the periods by means of a riskless storage technology or a risky asset with i.i.d. dividend payments. I analyze the dynamics of asset holdings and asset prices and identify the influence of the aspiration level, the length of memory and the form of the similarity function. The height of the aspiration level determines whether the economy exhibits constant prices and asset holdings or evolves in a cycle. The length of memory is associated with the ability of the investors to learn the correct distribution of returns, whereas the form of the similarity function influences the willingness of investors to diversify.

Evolution of Wealth and Asset Prices in Markets with Case-Based Investors

I analyze whether case-based decision makers (CBDM) can survive in an assetmarket in the presence of expected utilitymaximizers. Conditions are identified, under which the CBDM retain a positive mass with probability one. CBDM can cause predictability of asset returns, high volatility and bubbles. It is found that the expected utility maximizers can disappear from the market for a finite period of time, if the mispricing of the risky asset caused by the case-based decision-makers aggravates too much. Only in the case of logarithmic expected utility maximizers do the case-based decision makers disappear from the market for all parameter values.

Asset Prices in an Overlapping Generations Model with Case-Based Decision Makers with Short Memory

I consider an economy, populated by case-based decision makers with one-period memory. Consumption can be transferred between the periods by the means of a riskless storage technology or a risky asset with iid dividend payments. I analyze the dynamics of asset holdings and asset prices. Whereas an economy in which the investors have low aspiration levels exhibits constant prices and asset holdings, investors with high aspiration levels create cycles, which may be stochastic or deterministic. Arbitrage possibilities, deviation of the price from the fundamental value, predictability of returns and excessive volatility are shown to obtain in a market with case-based investors.

A Note on Case-Based Optimization with a Non-Degenerate Similarity Function

The paper applies the ��realistic-ambitious�� rule for adaptation of the aspiration level suggested by Gilboa and Schmeidler (1996) to a situation in which the similarity between the available acts is represented by a non-degenerate function. The paper shows that the optimality result obtained by Gilboa and Schmeidler (1996) in general fails. With a concave similarity function, the best corner act is chosen in the limit. Introducing convex regions into the similarity function improves the limit choice. A sufficiently fine similarity function allows to approximate optimal behavior with an arbitrary degree of precision.

Preference for Diversification with Similarity Considerations

The paper studies the connection between the form of the similarity function of a decision-maker and his willingness to diversify. It is shown that preference for diversification obtain for both high and low aspiration levels if the similarity function is convex in the Euclidean distance. However, a decision-maker with a concave similarity function and relatively high aspiration level will fail to choose diversified acts, even if his utility function is concave.

Multiple Priors as Similarity Weighted Frequencies

In this paper, we consider a decision-maker who tries to learn the distribution of outcomes from previously observed cases. For each observed sequence of cases the decision-maker predicts a set of priors expressing his beliefs about the underlying probability distribution. We impose a version of the concatenation axiom introduced in BILLOT, GILBOA, SAMET AND SCHMEIDLER (2005) which insures that the sets of priors can be represented as a weighted sum of the observed frequencies of cases. The weights are the uniquely determined similarities between the observed cases and the case under investigation.

A note on case-based optimization with a non-degenerate similarity function

The paper applies the "realistic-ambitious" rule for adaptation of the aspiration level suggested by Gilboa and Schmeidler (1996) to a situation in which the similarity between the available acts is represented by a non-degenerate function. The paper shows that the optimality result obtained by Gilboa and Schmeidler (1996) in general fails. With a concave similarity function, the best corner act is chosen in the limit. Introducing convex regions into the similarity function improves the limit choice. A sufficiently fine similarity function allows to approximate optimal behavior with an arbitrary degree of precision

Multiple Priors as Similarity Weighted Frequencies

In this paper, we consider a decision-maker who tries to learn the distribution of outcomes from previously observed cases. For each observed sequence of cases, the decision-maker entertains a set of priors expressing his hypotheses about the underlying probability distribution. The set of probability distributions shrinks when new information confirms old data. We impose a version of the concatenation axiom introduced in BILLOT, GILBOA, SAMET AND SCHMEIDLER (2005) which insures that the sets of priors can be represented as a weighted sum of the observed frequencies of cases. The weights are the uniquely determined similarities between the observed cases and the case under investigation.

Flexibility of Choice Versus Reduction of Ambiguity

This paper explores the problem of a social planner willing to improve the welfare of individuals who are unable to compare all available alternatives. The optimal decision trades off the individuals' desire for flexibility versus their aversion towards ambiguous choice situations. We introduce an axiom system that formalizes this idea. Our main result characterizes the preference maximizing opportunity set. It is a maximal set that consists of mutually comparable alternatives. It also has the property that it maximizes the sum of the distances between its ordered elements for some appropriate metric imposed on the set of possible choices.Incomplete preferences, ambiguity, ?exibility of choice, opportunity sets, uncertainty

Flexibility of Choice versus Reduction of Ambiguity

This paper explores the problem of a social planner willing to improve the welfare of individuals who are unable to compare all available alternatives. The optimal decision trades off the individuals' desire for flexibility versus their aversion towards ambiguous choice situations. We introduce an axiom system that formalizes this idea. Our main result characterizes the preference maximizing opportunity set. It is a maximal set that consists of mutually comparable alternatives. It also has the property that it maximizes the sum of the distances between its ordered elements for some appropriate metric imposed on the set of possible choices.