We provide a price characterization of efficient contingent claims-that is, chosen by at least a rational agent-in multiperiod economies with market frictions. Frictions include market incompleteness, transaction costs, short-selling, and borrowing costs. We characterize the inefficiency cost of a trading strategy-its required investment minus the largest amount necessary to obtain the same utility level-and we propose a measure of portfolio performance. We show that arbitrage bounds cannot be tightened based on efficiency without restricting preferences or endowments. We observe common investment strategies becoming inefficient with market frictions and others rationalized by them.

Given the exogenous price process of some assets, we constrain the price process of other assets that are characterized by their final payoffs. We deal with an incomplete market framework in a discrete-time model and assume the existence of the equilibrium. In this setup, we derive restrictions on the state-price deflators. These restrictions do not depend on a particular choice of utility function. We investigate numerically a stochastic volatility model as an example. Our approach leads to an interval of admissible prices that is more robust than the arbitrage pricing interval.

In this paper we provide a price characterization of efficient consumption bundles in multiperiod economies with market frictions. Efficient consumption bundles are those that are chosen by at least one rational agent with monotonic state-independent and risk-averse preferences and a given future endowment. Frictions include dynamic market incompleteness, proportional transaction costs, short selling costs, borrowing costs, taxes, and others. We characterize the inefficiency cost of a trading strategy -the difference between the investment it requires and the largest amount required by any rational agent to obtain the same utility level - and we propose a measure of portfolio performance based on it. We also show that the arbitrage bounds on a contingent claim to consumption cannot be tightened based on efficiency arguments without restricting preferences or endowments. We examine the efficiency of common investment strategies in economies with borrowing costs due to asymmetric information, short selling costs, or bid-ask spreads. We find that market frictions generally change and typically shrink the set of efficient investment strategies, shifting investors away from well-diversified strategies into low cost ones, and for large frictions into no trading at all. Hence we observe strategies that become inefficient with market frictions, as well as strategies that are rationalized by market frictions.

Can investors with irrational beliefs be neglected as long as they are rational on average? Do their trades cancel out with no consequences on prices, as implicitly assumed by traditional models? We consider a model with irrational investors, who are rational on average. We obtain waves of pessimism and optimism that lead to countercyclical market prices of risk and procyclical risk-free rates. The variance of the state price density is greatly increased. The long run risk-return relation is modified; in particular, the long run market price of risk might be higher than both the instantaneous and the rational ones.

We study securities market models with fixed costs. We first characterize the absence of arbitrage opportunities and provide fair pricing rules. We then apply these results to extend some popular interest rate and option pricing models that present arbitrage opportunities in the absence of fixed costs. In particular, we prove that the quite striking result obtained by Dybvig, Ingersoll, and Ross (1996), which asserts that under the assumption of absence of arbitrage long zero-coupon rates can never fall, is no longer true in models with fixed costs, even arbitrarily small fixed costs. For instance, models in which the long-term rate follows a diffusion process are arbitrage-free in the presence of fixed costs (including arbitrarily small fixed costs). We also rationalize models with partially absorbing or reflecting barriers on the price processes. We propose a version of the Cox, Ingersoll, and Ross (1985) model which, consistent with Longstaff (1992), produces yield curves with realistic humps, but does not assume an absorbing barrier for the short-term rate. This is made possible by the presence of (even arbitrarily small) fixed costs.

The aim of this paper is to analyse the impact of heterogeneous beliefs in an otherwise standard competitive complete market economy. The construction of a consensus probability belief, as well as a consensus consumer, is shown to be valid modulo an aggregation bias, which takes the form of a discount factor. In classical cases, the consensus probability belief is a risk tolerance weighted average of the individual beliefs, and the discount factor is proportional to beliefs dispersion. This discount factor makes the heterogeneous beliefs setting fundamentally different from the homogeneous beliefs setting, and it is consistent with the interpretation of beliefs heterogeneity as a source of risk. We then use our construction to rewrite in a simple way the equilibrium characteristics (market price of risk, risk premium, risk-free rate) in a heterogeneous beliefs framework and to analyse the impact of beliefs heterogeneity. Finally, we show that it is possible to construct specific parametrizations of the heterogeneous beliefs model that lead to globally higher risk premia and lower risk-free rates.

Why do investors keep different opinions even though they learn from their own failures and successes? Why do investors keep different opinions even though they observe each other and learn from their relative failures and successes? We analyze beliefs dynamics when beliefs result from a very general learning process that favors beliefs leading to higher absolute or relative utility levels. We show that such a process converges to the Nash equilibrium in a game of strategic belief choices. The asymptotic beliefs are subjective and heterogeneous across the agents. Optimism (respectively overconfidence) as well as pessimism (respectively doubt) emerge from the learning process. Furthermore, we obtain a positive correlation between pessimism (respectively doubt) and risk tolerance. Under reasonable assumptions, beliefs exhibit a pessimistic bias and, as a consequence, the risk premium is higher than in a standard setting.

This paper presents an equilibrium model in a pure exchange economy when investors have three possible sources of heterogeneity. Investors may differ in their beliefs, in their level of risk aversion, and in their time preference rate. The authors study the impact of investors’ heterogeneity on equilibrium properties and, in particular, on the consumption shares, the market price of risk, the risk-free rate, the bond prices at different maturities, the stock price and volatility as well as on the stock's cumulative returns, and optimal portfolio strategies. The authors relate the heterogeneous economy with the family of associated homogeneous economies with only one class of investors. Cross-sectional as well as long-run properties are analyzed.