Conditional Comonotonicity

In this paper we propose a generalization of the comonotonicity notion by introducing and exploring the concept of conditional comonotonicity. We characterize this notion and we show on examples that conditional comonotonicity is the natural extension of the concept of comonotonicity to dynamic settings.comonotonicity; dynamic comonotonicity

Arbitrage pricing and equilibrium pricing : compatibility conditions

The problem of fair pricing of contingent claims is well understood in the contex of an arbitrage free, complete financial market, with perfect information : the so-called arbitrage approach permits to construct a unique valuation operator compatible with observed price processes. In the more realistic context of partial information, the equilibrium analysis permits to construct a unique valuation operator which only depends on some particular price processes as well as on the dividends process. In this paper we present these two approaches and we explore their links and the conditions under which they are compatible ; In particular, we derive from the equilibrium conditions some links between the price processes paramaters and those of the dividend processes paramatersArbitrage, equilibrium, optimality, incomplete markets, nonredudant assets, derivatives pricing

On Abel's Concepts of Doubt and Pessimism.

In this paper, we characterize subjective probability beliefs leading to a higher equilibrium market price of risk. We establish that Abel's result on the impact of doubt on the risk premium is not correct in general; see Abel [2002. An exploration of the effects of pessimism and doubt on asset returns. Journal of Economic Dynamics and Control 26, 1075–1092]. We introduce, on the set of subjective probability beliefs, market-price-of-risk dominance concepts and we relate them to well-known dominance concepts used for comparative statics in portfolio choice analysis. In particular, the necessary first-order conditions on subjective probability beliefs in order to increase the market price of risk for all nondecreasing utility functions appear as equivalent to the monotone likelihood ratio property.Pessimism; Optimism; Doubt; Risk Premium; Stochastic Dominance; Market Price of Risk; Portfolio Dominance; Monotone Likelihood Ratio;

Aggregation of Heterogeneous Beliefs.

This paper is a generalization of [Calvet, L., Grandmont, J.-M., Lemaire, I., 2002. Aggregation of heterogenous beliefs and asset pricing in complete financial markets. Working paper] to a dynamic setting. We propose a method to aggregate heterogeneous individual probability beliefs, in dynamic and complete asset markets, into a single consensus probability belief. This consensus probability belief, if commonly shared by all investors, generates the same equilibrium prices as well as the same individual marginal valuation as in the original heterogeneous probability beliefs setting. As in [Calvet, L., Grandmont, J.-M., Lemaire, I., 2002. Aggregation of heterogenous beliefs and asset pricing in complete financial markets. Working paper], the construction stands on a fictitious adjustment of the market portfolio. The adjustment process reflects the aggregation bias due to the diversity of beliefs. In this setting, the construction of a representative agent is shown to be also valid.Representative agents; Aggregation of belief; Consensus belief; Heterogeneous beliefs;

Unbiased Disagreement in financial markets, waves of pessimism and the risk return tradeoff

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 mod- i…ed; in particular, the long run market price of risk might be higher than both the instantaneous and the rational ones.irrational investors, rational on average

Strategic Beliefs

We provide a discipline for beliefs formation through a model of subjective beliefs, in which agents hold incorrect but strategic beliefs. More precisely, we consider beliefs as a strategic variable that agents can manipulate to maximize their utility from trade. Our framework is therefore an imperfect competition framework, and the underlying concept is the concept of Nash equilibrium. We find that a strategic behavior leads to beliefs subjectivity and heterogeneity. Optimism (resp. overconfidence) as well as pessimism (resp. doubt) both emerge as optimal beliefs. Furthermore, we obtain a positive correlation between pessimism (resp. doubt) and risk-tolerance. The consensus belief is pessimistic and, as a consequence, the risk premium is higher than in a standard setting. Our model is embedded in a standard financial markets equilibrium problem and may be applied to several other situations in which agents have to choose the optimal exposure to a risk (choice of an optimal retention rate for an insurance company, choice of the optimal proportion of equity to retain for an entrepreneur and for a given project)Beliefs, Strategic, Pessimism, Consensus, Risk-premium, Heterogeneous, Doubt, Overconfidence

Arbitrage and state price deflators in a general intertemporal framework

In securities markets, the characterization of the absence of arbitrage by the existence of state price deflators is generally obtained through the use of the Kreps–Yan theorem.This paper deals with the validity of this theorem (see Kreps, D.M., 1981. Arbitrage and equilibrium in economies with infinitely many commodities. Journal of Mathematical Economics 8, 15–35; Yan, J.A., 1980. Caractérisation d'une classe d'ensembles convexes de L1 ou H1. Sém. de Probabilités XIV. Lecture Notes in Mathematics 784, 220–222) in a general framework. More precisely, we say that the Kreps–Yan theorem is valid for a locally convex topological space (X,?), endowed with an order structure, if for each closed convex cone C in X such that CX? and C?X+={0}, there exists a strictly positive continuous linear functional on X, whose restriction to C is non-positive.We first show that the Kreps–Yan theorem is not valid for spaces if fails to be sigma-finite.Then we prove that the Kreps–Yan theorem is valid for topological vector spaces in separating duality X,Y, provided Y satisfies both a “completeness condition” and a “Lindelöf-like condition”.We apply this result to the characterization of the no-arbitrage assumption in a general intertemporal framework.Arbitrage; State price deflators; Free lunch; Fundamental theorem of asset pricing; Investment opportunities

Aggregation of Heterogeneous Beliefs

This paper is a generalization of [Calvet, L., Grandmont, J.-M., Lemaire, I., 2002. Aggregation of heterogenous beliefs and asset pricing in complete financial markets. Working paper] to a dynamic setting. We propose a method to aggregate heterogeneous individual probability beliefs, in dynamic and complete asset markets, into a single consensus probability belief. This consensus probability belief, if commonly shared by all investors, generates the same equilibrium prices as well as the same individual marginal valuation as in the original heterogeneous probability beliefs setting. As in [Calvet, L., Grandmont, J.-M., Lemaire, I., 2002. Aggregation of heterogenous beliefs and asset pricing in complete financial markets. Working paper], the construction stands on a fictitious adjustment of the market portfolio. The adjustment process reflects the aggregation bias due to the diversity of beliefs. In this setting, the construction of a representative agent is shown to be also valid.Heterogeneous beliefs; Consensus belief; Aggregation of belief; Representative agents

Are More Risk-Averse Agents More Optimistic? Insights from a Simple Rational Expectations Equilibrium Model

We analyze the link between pessimism and risk-aversion. We consider a model of partially revealing, competitive rational expectations equilibrium with diverse information, in which the distribution of risk-aversion across individuals is unknown. We show that when a high individual level of risk-aversion is taken as a signal for a high average level of risk-aversion, more risk-averse agents are more optimistic. This correlation between individual risk-aversion and optimism leads to a pessimistic consensus belief hence to an increase in the market price of risk. Risk-sharing schemes and welfare implications are analyzed. We show that agents' welfare may increase upon the receipt of more precise information.Optimism, risk-aversion, rational expectations, risk-premium, heterogenous beliefs

Gurus and beliefs manipulation

We analyze a model with two types of agents: standard agents and gurus, i.e. agents who have the ability to influence the other investors. Gurus announce their beliefs and act accordingly. Each investor has a preferred guru and follows his recommendations. Prices are determined through a classical Walras mechanism. Gurus are strategic: they take into account the impact of their announced beliefs on the other agents, hence on prices. At the Nash equilibrium, this leads to beliefs heterogeneity, to a positive correlation between optimism and risk aversion and to higher risk premia. The impact is stronger on the riskier assets.standard agents ; gurus ; Walras mechanism ; riskier assets