Clotilde Napp

The Dalang–Morton–Willinger theorem under cone constraints

The Dalang–Morton–Willinger theorem [Stochastics Stochastic Rep. 29 (1990) 185] asserts, for a discrete-time perfect market model, that there is no arbitrage if and only if the discounted price process is a martingale with respect to an equivalent probability measure. The financial market is supposed to be perfect in the sense that there is no transaction cost, no imperfection on the numeraire, no short sale constraint, no constraint on the amounts invested, etc.In this note, we explore the same issue in the presence of such imperfections, more precisely, in the presence of polyhedral convex cone constraints. We first obtain a generalization of the Dalang–Morton–Willinger theorem [Stochastics Stochastic Rep. 29 (1990) 185]: we prove that under polyhedral convex cone constraints, absence of arbitrage is equivalent to the existence of a discount process such that, taking this process as a deflator, the net present value of any available investment opportunity is nonpositive.We then apply this general result to specific market imperfections fitting in the convex cone framework, like short sale constraints, solvability constraints, constraints on the quantities, amounts or proportions invested. We improve a result of Pham–Touzi [J. Math. Econ. 31 (2) (1999) 265]. We show that our model enables to deal with financial markets with possible imperfections on the numeraire (like different borrowing and lending rates, or more general convex cone constraints involving the numeraire).

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 modified; in particular, the long run market price of risk might be higher than both the instantaneous and the rational ones.

Arbitrage and Viability in Securities Markets with Fixed Trading Costs

This paper studies foundational issues in securities markets models with fixed costs of trading, i.e. transactions costs that are bounded regardless of the transaction size, such as fixed brokerage fees, investment taxes, operational, and processing costs or opportunity costs. We show that the absence of free lunches in such models is equivalent to the existence of a family of absolutely continuous probability measures for which the normalized securities price processes are martingales. This is a weaker condition than the absence of free lunch in frictionless models, which is equivalent to the existence of an equivalent martingale measure. We also show that the only arbitrage-free pricing rules on the set of attainable contingent claims are those that are equal to the sum of an expected value with respect to any absolutely continuous martingale measure and of a bounded fixed cost functional. Moreover, these pricing rules are the only ones to be viable as models of economic equilibrium.

Is There a Pessimistic Bias in Individual Beliefs? Evidence from a Simple Survey

Cf. papier Is There a Pessimistic Bias in Individual Beliefs? Evidence from a Simple Survey

Discounting and Divergence of Opinion

The objective of this paper is to adopt a general equilibrium model and determine the socially efficient discount factor, risk free rate and discount rate when there are heterogeneous anticipations about the growth of the economy as well as heterogeneous time preference rates. Among others we tackle the following questions. Is the socially efficient discount factor an arithmetic average of the individual subjectively anticipated discount factors‘ More generally, can the Arrow-Debreu prices, the risk free rates, the subjectively expected socially efficient discount factors and discount rates be obtained as an average of the individual subjectively anticipated ones‘ Can beliefs dispersion be analyzed as a sort of additional risk or uncertainty leading to possibly lower discount rates‘ Is it socially efficient, when diversity of opinion is taken into account, to reduce the discount rate per year for more distant horizons‘ If so, what is the trajectory of the decline‘

On Abel's concept of doubt and pessimism

In this paper, we characterize subjective probability beliefs leading to a higher equilibrium market price of risk. We establish that Abels result on the impact of doubt on the risk premium is not correct (see Abel, A., 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.

Are risk-averse agents more optimistic? A Bayesian estimation approach

Our aim is to analyze the link between optimism and risk aversion in a subjective expected utility setting and to estimate the average level of optimism when weighted by risk tolerance. This quantity is of particular importance since it characterizes the consensus belief in risk-taking situations with heterogeneous beliefs. Its estimation leads to a nontrivial statistical problem. We start from a large lottery survey (1,536 individuals). We assume that individuals have true unobservable characteristics and that their answers in the survey are noisy realizations of these characteristics. We adopt a Bayesian approach for the statistical analysis of this problem and use an hybrid MCMC approximation method to numerically estimate the distributions of the unobservable characteristics. We obtain that individuals are on average pessimistic and that pessimism and risk tolerance are positively correlated. As a consequence, we conclude that the consensus belief is biased towards pessimism.

Pricing issues with investment flows Applications to market models with frictions

Abstract In this paper, we study some foundational issues in the theory of asset pricing. We consider a model where any investment opportunity is described in terms of cash flows. We do not assume that there is a numeraire, the time horizon is not supposed to be finite, the investment opportunities are not specifically related to the buying and selling of securities on a financial market. In this quite general framework, we consider different possible definitions of admissible prices for a contingent flow, mainly related to arbitrage and equilibrium considerations, and for each possible definition, we characterize the set of admissible prices. Since most market imperfections, such as short sale constraints, convex cone constraints, proportional transaction costs, no borrowing or different borrowing and lending rates, etc., can fit in the preceding model for a specific set of investment opportunities, our approach with flows provides a unified framework for the study of pricing issues in market models with frictions (including imperfections on the numeraire). We generalize existing results and we obtain them all in a unified way.

Evolutionary beliefs and financial markets

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.

On multivariate prudence

In this note we extend the theory of precautionary saving to the case of multivariate risk. We introduce a notion of multivariate prudence, related to a precautionary premium, and we propose a matrix-measure to capture the strength of the precautionary saving motive. We discuss the usefulness of this measure, in particular for comparing precautionary behavior among individuals. We also characterize the notion of multivariate downside risk aversion as a preference for disaggregating harms across outcomes of multivariate lotteries. We show the link between this notion and the notion of multivariate prudence, we propose a matrix-measure of its intensity, and we illustrate the usefulness of our results in a problem of social discounting.