JOUINI Elyes

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In both arbitrage and utility pricing approaches, the fictitious completion appears as a powerful tool that permits to extend complete markets results to an incomplete markets framework. Does this technique permit to characterize the equilibrium pricing interval? This note provides a negative answer.

The so-called “gender-equality paradox” is the fact that gender segregation across occupations is more pronounced in more egalitarian and more developed countries. Some scholars have explained this paradox by the existence of deeply rooted or intrinsic gender differences in preferences that materialize more easily in countries where economic constraints are more limited. In line with a strand of research in sociology, we show instead that it can be explained by cross-country differences in essentialist gender norms regarding math aptitudes and appropriate occupational choices. To this aim, we propose a measure of the prevalence and extent of internalization of the stereotype that “math is not for girls” at the country level. This is done using individual-level data on the math attitudes of 300,000 15-y-old female and male students in 64 countries. The stereotype associating math to men is stronger in more egalitarian and developed countries. It is also strongly associated with various measures of female underrepresentation in math-intensive fields and can therefore entirely explain the gender-equality paradox. We suggest that economic development and gender equality in rights go hand-in-hand with a reshaping rather than a suppression of gender norms, with the emergence of new and more horizontal forms of social differentiation across genders.

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The purpose of this paper is to analyze the consequences of introducing heterogeneous risk and time perceptions (beliefs, impatience rates) in standard valuation models. We first show that the various arguments put forward in the literature to deny this heterogeneity or to neglect its effects are contradicted both by the data and by the most recent work. We then introduce a typology of these perceptions, analyze their various forms and study how the market aggregates them. We deduce the impact of this heterogeneity of perceptions on the risk premium (or the market price of risk) and on the price of time (discount rate or interest rate). In particular, we show that in the long run, the diversity of perceptions should lead to a more conservative valuation: lower discount rate and higher risk premium.

We study the effects of the presence of a negative stereotype on the formation of self-confidence and on decision-making in achievement-related situations. We take into account not only consumption utility but also psychological utility (ex-ante ego utility and ex-post disappointment/elation). We show that any stereotype of lower ability (in the form of biased interpretation of success and failure in terms of ability) leads to gaps in confidence, in participation in risky/ambitious options and in performance. Furthermore, we show how the stereotype survives and even gets reinforced. Considering gender and mathematics, we are able to explain the lower self-confidence of girls in mathematics, their underrepresentation in STEM fields, as well as their choices of less ambitious options and lower performance.

While gender gaps in average math performance are now close to zero in developed countries, women are still strongly underrepresented among math high performers (1). This gender gap contributes to the underrepresentation of women in math and science in higher education and to their subsequent worse position in the labor market (2, 3). With the roles of nature and nurture (4–6) on gender performance gaps having been debated for more than a century, research in the 1990s and 2000s (7–9) suggested a cultural origin, relating gender gaps in math to measures of countries' gender inequality. However, with more recent studies (10–12) having shown that this relation is weak, today we have no clearly identified relationship between countries' socioeconomic or cultural environment and the gender gap in math. We relate below gender gaps in math to societal inequalities that are not directly related to gender. We find a strong and robust relationship and provide tests suggesting that it is causal: Countries that are generally more egalitarian, or that have institutions more conductive to equality, have a lower gender performance gap in math, suggesting that this gap is partly shaped by more general societal inequalities.

The under-representation of women in scientific fields, which are the most prestigious and most financially rewarding, is an indisputable fact. Yet the reasons why this should be so are still poorly understood. This synthesis of the many studies on gender seeks to deconstruct stereotypes. In the light of their findings, the aim is to identify relevant and effective public policy measures for reducing the gender gap. The under-representation of women in science is of considerable importance, since it largely explains gender asymmetries in professional life and in managerial circles. The challenge is therefore twofold: not only to eliminate unfair gender inequalities, which are of course inconsistent with republican principles, but also to ensure that society is in a position to mobilize the best possible skills.The publication by the Institut Louis Bachelier of this issue of Opinions et Débats may at first sight seem surprising. What is the connection between this topic and the ILB’s core area of interest, namely finance? One answer concerns the mathematical dimension, which is crucial for modern finance. And let us not forget that Louis Bachelier was a mathematician. A second answer is directly related to gender issues and probably partly explained by the first: there are very few women in the upper echelons of the financial industry. Thirdly – and this is possibly the most important point, because the ILB is a research network – recent work on gender issues draws upon, as one might expect, disciplines such as sociology and psychology, as well as decision theory and the concepts of risk, hedging and subjective probability, all of which play a key role in financial research and borrow some models from it.

We present a theoretical model of health beliefs and behaviors that explicitly takes into account the emotional impact of possible bad news (i.e., illness), ex-ante in the form of anxiety and ex-post in the form of disappointment. Our model makes it possible to explain (simultaneously) a number of anomalies such as ’low’ testing rates, heterogeneous perceptions of risk levels, underestimation of health risk, ostriches and hypochondriacs, over-use and under-use of health services, patient preference for information when relatively certain of not being ill, yet avoiding information when relatively certain of being ill, etc. Our model matches observed patterns both in health beliefs and health behaviors and irrational health beliefs and behaviors can be characterized as the optimal response under a given structure of emotions and preferences.

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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.

We discuss Oster et al.’s (2013) model and propose an alternative model of optimal expectations to accommodate data on genetic testing.

At first glance the picture is dark. The Tunisian economy is now in very bad shape. An economic policy that favored the rent for the benefit of a minority has been replaced by a short-term policy that is not clear. The social situation is worrying and discontent is growing. Growth, slowed down and unevenly distributed, is insufficient. Europe is in crisis and the external engines of growth have disappeared. Investment is also at its lowest. The margins of maneuver are shrinking, the deficit is increasing, the debt is growing, prices are soaring and unemployment is reaching historic levels. And yet, there is hope! The potentials are recognized and the opportunities are real: Tunisia can claim to double its wealth in few years. The urgency is to think differently and to engage without further delay. While taking care to remain attentive, pragmatic and daring, this book proposes - better than reforms - a real change: an energetic overhaul of educational choices, tax policy, the health system, and solidarity mechanisms. And, with the aim of transforming Tunisia into a real regional exporting power, it rethinks the supply and quality of services, readapts agriculture to the customer and the climate, remodels the techno-industrial landscape, reconsiders the territory.Elyes Jouini, as a man of science and field, surrounded by the best experts in the fields at stake, proposes in parallel to the undeniable political maturity of Tunisia, a regeneration of its economy and provides the instructions for use. This new vision would allow to anchor Tunisia in an accelerated, perennial, balanced growth and whose fruits would be redistributed in the fairest possible way.The revolution made the unthinkable possible, it remains for us to make possible the essential and the necessary.The time has come!

Islamic and conventional investment funds are similar in that they have the same purpose. However, unlike conventional funds, Islamic funds are required to invest according to a set of selection rules. This thesis is interested in developing a theoretical and empirical framework to explain the management fees, performance and risk of investment funds. Thus, this work begins by developing a theoretical analysis of profit and loss sharing contracts (venture contracts) confronted with asymmetric information problems. A theoretical model, in the presence of adverse selection problems between the manager and the investor, shows that the respective degrees of risk aversion of the manager and the investor have an impact on the negotiation of management fees indexed on the periodic performance of the fund (carried interest). The findings of this model lead us to empirically explain the choice of fund partners regarding the remuneration clauses, performance and risk of investment funds. To do so, we develop a unique database that includes an international sample of Islamic and conventional funds grouped by management company. By distinguishing between Islamic and conventional funds, the legal framework, political and economic conditions explain their fees, performance and risks.

We address the problem of a social planner who, as in Weitzman (2001), gathers data on experts’ discount rates and wants to infer the socially efficient consumption discount rate. We propose an ‘equilibrium approach’ and we analyse the expression and the properties of the resulting ‘equilibrium discount rate’. We compare our expression for the discount rate with the different expressions that have been previously proposed in the literature. We analyse the impact of shifts in the distributions of experts discount rates. Finally, we apply our approach to Weitzman (2001)’s data to propose discount rates for public sector Cost-Bene…t Analysis, in particular for the long term.

In this article, we focus on the role of the state in financing the economy and emphasize the need for the government to take a long-term view that integrates financial markets, public-private partnerships and external financing. We also propose to focus on the banking sector and insist in particular on the need for a joint strategy involving the Ministry of Economy and Finance and the Central Bank.

This thesis studies portfolio choice and asset pricing with preferences that go beyond standard expectation-utility and mean-variance preferences. The first part of this thesis focuses on a decision model in which the decision maker forms endogenous beliefs given his expectation utility and hindsight deception. The implications of the model for portfolio choice and asset pricing are derived and compared to the implications of the standard utility expectation model. The second part of this thesis focuses on investors who derive the utility of the first three moments of their portfolio returns. We derive and test the conditions under which additional assets can improve the investment universe of investors with mean-variance-skewness preferences. The implications of these preferences for equilibrium asset returns are then analyzed and tested with stock market returns.

We revisit the model proposed by Gollier and Muermann (see Gollier, C. and A. Muermann, 2010, Optimal choice and beliefs with exante savoring and ex-post disappointment, Management Sci., 56, 1272-1284, hereafter GM). In GM, for a given lottery, agents form anticipated expected payoffs and the set of possible anticipations is assumed to be exogenously fixed. We rather propose sets of possible anticipations which are endogenously determined. This permits to compare and evaluate in a consistent manner lotteries with different supports and to revisit the portfolio choice problem. We obtain new conclusions and interesting insights. Our extended model can rationalize a variety of empirically observed puzzles like a positive demand for assets with negative expected returns, preference for skewed returns and under-diversification of portfolios.

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In this paper we analyse the risk attitude of a group of heterogenous agents and we develop a theory of comparative collective risk tolerance. In particular, we characterize how shifts in the distribution of individual levels of risk tolerance affect the representative agent's degree of risk tolerance. In the model with efficient risk - sharing and two agents (e.g. a household) with isoelastic preferences we show that an increase of the level of risk tolerance of one of the agents might have an ambiguous impact on the aggregate level of risk tolerance. the latter increases for some levels of aggregate wealth while it decreases for other levels of aggregate wealth. Specifically, there are two possible shapes for aggregate risk tolerance as a function of the risk tolerance level of one of the agents: increasing curve or increasing then decreasing curve. For more general populations we characterize the effect of first order like shifts (individual levels of risk tolerance more concentrated on high values) and second order like shifts (more dispersion on individual levels of risk tolerance) on the collective level of risk tolerance. We also evaluate how shifts in the distribution of individual levels of risk tolerance impact the collective level of risk tolerance in a framework with exogenous egalitarian sharing rules. Our results permit to better characterize differences in risk taking behavior between groups and individuals and among groups with different distribution of risk preferences.

Kimball (1990) established that income risk increases the marginal propensity to consume if and only if absolute prudence is decreasing. We characterize decreasing and increasing multivariate prudence and we show that a multidimensional risk increases the marginal propensity to consume if and only if a matrix-measure of multivariate prudence decreases with wealth, in the sense that its derivative is negative-de…nite.

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 (resp. overconfidence) as well as pessimism (resp. doubt) both emerge from the learning process. Furthermore, we obtain a positive correlation between pessimism (resp. 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.

In this article, we characterize efficient portfolios, i.e. portfolios which are optimal for at least one rational agent, in a very general financial market model of foreign currencies with proportional transaction costs. In our setting, transaction costs may be random, time dependent, have jumps and the preferences of the agents are modeled by multivariate expected utility functions. Thanks to the dual formulation of expected multivariate utility maximization problem established in Campi and Owen, we provide a complete characterization of efficient portfolios, generalizing earlier results of Dybvig and Jouini and Kallal. We basically show that a portfolio is efficient if and only if it is cyclically anticomonotonic with respect to at least one consistent price system. Finally, we introduce the notion of utility price of a given contingent claim as the minimal amount of a given initial portfolio allowing any agent to reach the claim by trading in the market, and give a dual representation of it.

Kimball (1990a,b) established that income risk increases the marginal propensity to consume if and only if absolute prudence decreases. We characterize decreasing and increasing multivariate prudence and show that a multidimensional risk increases the marginal propensity to consume if and only if absolute prudence decreases with wealth, in the sense that its derivative is negative-definite.

In this paper we extend the theory of precautionary saving to the case in which uncertainty is multidimensional and we develop a matrix-measure of multivariate prudence. Furthermore, we characterize comparative prudence, decreasing and increasing prudence, the effect of uncertainty on the marginal propensity to consume out of wealth, and the Drèze-Modigliani substitution effect in this multivariate setting. We also characterize the concept of multivariate downside risk aversion as a multivariate preference for harm disaggregation. We show that our definition is equivalent to a positive precautionary saving motive. We propose an alternative measure of the intensity of downside risk aversion and show that this measure is useful in understanding several economic problems that involve multivariate preferences.

We study comparative statics of Nth-degree risk increases within a large class of problems that involve bidimensional payoffs and additive or multiplicative risks. We establish necessary and sufficient conditions for unambiguous impact of Nth-degree risk increases on optimal decision making. We develop a simple and intuitive approach to interpret these conditions : novel notions of directional Nth-degree risk aversion that are characterized via preferences over lotteries.

The thesis studies the impact of heterogeneous beliefs on the characteristics of equilibrium economies composed of irrational agents. In the first part, we analyze an equilibrium economy composed of two agents, one optimistic and the other pessimistic, investing in an unlimited supply production and a net zero supply bond. The optimal investments of the optimist (pessimist) in production and in the bond are respectively higher (low) and lower (high) than in the rational case. The risk-free rate is an average of the homogeneous rates of single-agent economies, weighted by the shares of total wealth that each agent holds. The rate, which is pro-cyclical, fluctuates between the rate of the optimist (upper bound) and the pessimist (lower bound). The fluctuations of the rate and the share of total wealth invested in the bond increase with increasing divergence of beliefs. A near-zero wealth agent has the largest impact on the characteristics. In the second part, we study an equilibrium economy composed of agents with subjective and heterogeneous beliefs. The agents, individually irrational but collectively rational, share an endowment generated by two sources of risk. Risk premiums and the risk-free rate are averages of their levels analogous to those in one-agent economies, weighted by each agent's share of the endowment. They are on average equal to their rational values and have a pro- or counter-cyclical behavior defined by beliefs. Greater divergence in beliefs creates greater uncertainty and volatility in asset prices.

In this thesis, we propose to test a new behavioral explanation of the risk premium puzzle. This work is based on the heterogeneous belief model of Jouini and Napp (2007) according to which investors' pessimism at the aggregate level leads to the existence of very large risk premiums. In this model, the pessimism of agents results in an underestimation of the rate of return on assets: thus, while they demand a return on risk identical to that of a standard agent, pessimistic agents overestimate the risk associated with assets and the resulting risk premium is increased. The conclusions of this model are obtained in the absence of individual pessimism among all agents, since the increase in the price of risk results from pessimism at the aggregate level, which resides in the positive correlation between optimism and risk aversion. Based on this observation, we identify the conditions under which excess returns on securities are consistent with agents' pessimism. We investigate whether the positive correlation between optimism and risk aversion is obtained in survey and laboratory experiments.

We analyze through the prism of general economic equilibrium theory the consequences of the opening of new markets, such as emission rights, instituted in the framework of climate change mitigation and adaptation policies. In the first chapter we introduce a theoretical framework for the analysis: an economy with extemalities and increasing returns. We establish an index formula and obtain as a corollary the existence of general pricing equilibria. In the second chapter, the opening of a rights market appears as a disturbance of this initial equilibrium situation. We then describe the changes in firms' choices that guarantee the existence of an equilibrium in the extended economy. In the third chapter, we analyze the influence of the opening of the rights market on the Pareto optimality of marginal pricing equilibria in the economy. It turns out that Pareto optima can be decentralized thanks to the fact that by setting a maximum level of pollution, the government provides the economy with a free public good consisting of the difference between this level and the situation prevailing under laissez-faire. In the last chapter, we extend the Pareto Optima decentralization problem to the case where the production capacities taken into account in the definition of optimality differ from those perceived by firms. This framework is developed to account for the apparently divergent expectations of firms and governments about the economic consequences of climate change.

This thesis focuses on applications of comonotonicity in finance. In the first chapter, we use this notion to characterize the efficient random wealth, solutions of a budget constrained utility maximization problem, for markets with frictions. We derive a measure of inefficiency, not based on any particular utility. Applying these results, we study efficiency in the context of diffusion models. In the second chapter, we study efficiency in models with transaction costs. Considering multidimensional utility functions, we show that efficiency is then characterized by cyclical comonotonicity. Finally, in the last chapter, assuming that only the historical distribution of a risky asset at maturity, the value of the forward, and the price of a European call option are known, we bound the smile using a comonotonicity hypothesis.

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This book focuses on the valuation and hedging of non-market financial options, the real options, which are used to evaluate optimal investment decisions. The objective of this thesis is to show how real options theory benefits from the contributions of probabilistic methods used for exotic options. The classical approach to real options favors the use of differential equation techniques, and we propose to evaluate investment projects by applying highly probabilistic methods. This distinction allows us to generalize the classical approach to the problem, and to obtain analytical results in situations where a differential equation technique would not allow it. We address the valuation of investment projects under certain specific constraints: when there is an incompressible time lag between the decision and its implementation, when there is competition between actors with different characteristics, and when the market information is imperfect. We also study hedging problems: how to hedge complex real options in the most efficient way when there are transaction costs, and how a new class of derivatives that are similar to barrier options can hedge the risk associated with the exercise of real options. Finally, we consider the optimal investment decision when the market can be manipulated. An economic agent with privileged information can intervene in the market and influence the value of securities. The mathematical tools used are mainly probabilistic, mainly excursion theory, local time and stochastic control. Several new results are demonstrated, in particular concerning Brownian transit times and excursion theory.

This thesis deals with option pricing problems in incomplete markets. It is divided into two parts, one dealing with generic incomplete problems in discrete time and the second with special cases of imperfections in continuous time. In the first part, the fundamental assumption is the equilibrium between supply and demand. In a multi-period model based on consumption, an agent seeks to value a financial product by maximizing his marginal utility at each date. In markets where only the process actually followed by the underlying asset is known, the arbitrage conditions do not sufficiently constrain the space of admissible "risk-neutral" probabilities. We show that, in several situations, the equilibrium assumption allows us to reduce this space by using the necessary properties satisfied by the admissible transition probabilities and to obtain a narrower range of prices, without specifying the agent's utility function (VNM). In the second part of the paper, we are interested in incompleteness situations arising from imperfections in the coverage of the derivative to be valued. The problems studied are those of transaction costs and illiquidity on the underlying. We treat the seller's problem by an optimal control procedure on the control variables. In the situation with transaction costs, we show that the use of a correlated asset in the hedge is a simple method to reduce the risk premium and thus be more competitive. In the context of a market with restrictions on the quantity of the underlying asset traded, management is more "static" than in the unconstrained setting. Our results allow us to better represent the management methods used in the markets, while keeping the parameterization simple, since we only add the agent's risk aversion factor.

We propose mathematical models applied to the management of pension funds, and more generally to the management of financial institutions with a long time horizon (30 or 40 years). In the first part we explain the optimal investment strategy for the consumption-investment problem when interest rates follow the (stochastic) dynamics proposed by Cox, Ingersoll and Ross (1985) and when the utility function is of the HARA or exponential type. The approach used is the martingale approach developed by Karatzas et al ( 1987) in the context of complete markets. We then extend the results in two directions: multifactor rate structure and more general utility functions. As an application, we consider the case of pension funds with defined contributions and a guaranteed minimum. In the second part, we focus on market incompleteness. We introduce a criterion, which we call Conditional Dominance, that allows us to obtain bounds on the value of any contingent asset. These bounds do not depend on the characteristics of the agents and in some cases they are strictly better than those obtained by over-replication. As an application, we consider the case of a defined benefit pension fund. Using the conditional dominance criterion, we can explicitly find the upper bound for the defined benefit value, as well as the hedging strategy.

This thesis is divided into two parts. The first part is devoted to the study of reinsurance markets in the presence of short selling. We take up the dynamic formalism introduced by Aase(1992), which uses marked point processes to represent the insured risk. We study the concept of competitive equilibrium in this particular type of exchange economy. We introduce the impossibility for companies to reinsure more contracts than they own. This assumption radically changes the nature of the problem, bringing a form of dynamic incompleteness. In the first chapter, we give necessary equilibrium conditions on the reinsurance premium. The second chapter considers the opposite question and gives sufficient conditions for the existence of a competitive equilibrium. The third chapter focuses on the implementation of competitive equilibria through a strategic market game. The second part focuses on the behavior of an investor wishing to hedge a contiguous act, when he does not know perfectly the underlying probabilistic model. We adopt a minimax approach, introduced by Karatzas and Cvitanic (1998). The agent does not know the risk-neutral probabilities. He then assumes that the "Market" is playing against him, by choosing a probability to maximize the hedging error. We thus see a zero-sum game between a fictitious player and the investor. When it admits a value, this value provides an upper bound to the hedging error. We show the existence of this value and analyze its properties. Finally, we consider an unknown parameter (volatility, trend) for which the agent adopts a Bayesian behavior. The two forms of attitudes towards uncertainty (minimax and Bayesian approach) are made to coexist by studying a zero-sum game with asymmetric information, for which we prove the existence of the value.

This paper consists of five parts and is particularly interested in the characterization of the no-arbitrage hypothesis in imperfect markets. This hypothesis imposes that one cannot make money out of nothing. The first part introduces the problem that concerns us and positions it in relation to the literature. In the second part, we establish a non-arbitrage theorem in a general framework for finite and discrete models. By applying it to different cases of imperfect markets, we recover the results of the literature and new properties on taxes. To do so, we use an adapted version of the Farkas lemma, results on optimal stopping, and properties of martingales. The next two parts are devoted to the study of a model such that each investment flow can be initiated at any date and in any state of the world under the same (stationary) conditions. The associated model is then necessarily infinite horizon. In the third part, we place ourselves in a deterministic framework. Thanks to the use of radon measurements, we study both the case of discrete and continuous dates. We demonstrate a non-arbitrage result. To do so, we use the properties of radon measurements. Then, in order to be able to 'separate' (c. F. Bourbaki e. V. T) the positive orthant and the set of payments, we show that the latter is locally compact as a compact sole cone. We also use properties of the Laplace transform. In the fourth part, we prove a non-arbitrage result in a stochastic but discrete setting, thanks to our farkas lemma and the brouwer theorem. Then, we apply it to the case of a financial market with transaction costs, which turns out to be stationary. We then obtain stronger results than those already existing in the literature. In the fifth and last part, we give a characterization of the absence of arbitrage when trading strategies are constrained to belong to a convex set. To this end. We show a closure result and then use a separation theorem from Yan (1980). Finally, we give a dual representation of the over-replication cost for a contingent asset.