REY FOURNIER Beatrice

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The value of a statistical life (VSL) is a key parameter in the analysis of government policy. Most policy decisions are made under ambiguity. This paper studies the effect of changes in ambiguity perception on the value of a statistical life (VSL). We propose a definition of increases in ambiguity perception based on Ekern’s (1980) definition of increases in risk. Ambiguity aversion alone is not sufficient to lead to an increase in the VSL when the decision maker perceives more ambiguity. Our results highlight the importance of higher order ambiguity attitudes, particularly ambiguity prudence.

This doctoral thesis starts from the observation that a credit portfolio is subject to several risks that come mainly from the credit quality of the borrower and its drawing and prepayment behavior on its credit lines. It turns out that the observed risks are dynamic and depend on various factors, both micro and macro-economic. We wanted to understand the articulation of these risks to have an effective management of them in the present, but also a prospective vision if the economic conditions change, for a proactive management. To address this issue, we have structured our research around three axes that have resulted in three chapters in the form of articles.(i) Analysis of changes in credit ratings as a function of risk factors.The use of multi-factor migration models has allowed us to reproduce stylized facts cited in the literature and to identify others. We also reconstruct the business cycle between 2006 and 2014 which manages to capture the 2008 and 2012 crises.(ii) Design of a cash flow model that accounts for the evolution of borrowers' behaviors under the influence of their micro and macroeconomic environments.We prove the influence of credit rating, business cycle, estimated recovery rate and short term interest rate on utilization rates. This model also allows us to obtain risk measures such as Cash Flow-at-Risk and Stressed Cash Flow-at-Risk on credit portfolios through Monte Carlo simulations.(iii) Reflecting on the Disposition-to-Pay (DTP) of an ambiguity-neutral decision maker to reduce risk in the presence of uncertainty on probabilities. We show that the presence of multiple (possibly correlated) sources of ambiguity changes the welfare of a risk-averse decision maker even though the decision maker is ambiguity neutral.

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The distribution of incomes of a population, the distribution of failure times of a material and the evolution of profits of life insurance contracts - studied in economics and management - are related to continuous functions belonging to the class of distribution functionals. Our thesis deals with the kernel estimation of distribution functionals with applications in economics and management sciences. In the first chapter, we propose local polynomial estimators in the i.i.d. framework of two distribution functionals, denoted LF and TF , useful to produce smooth estimators of the Lorenz curve and the scaled total time on test transform. The estimation method is described in Abdous, Berlinet and Hengartner (2003) and we prove the good asymptotic behavior of local polynomial estimators. Until then, Gastwirth (1972) and Barlow and Campo (1975) had defined piecewise continuous estimators of the Lorenz curve and the total normalized test time, which did not respect the continuity property of the initial curves. Illustrations on simulated and real data are proposed. The second chapter aims at providing local polynomial estimators in the i.i.d. framework of the successive derivatives of the distribution functionals explored in the previous chapter. Apart from the estimation of the first derivative of the TF function, which is treated using the smooth estimation of the distribution function, the estimation method employed is the local polynomial approximation of the distribution functionals detailed in Berlinet and Thomas-Agnan (2004). Various types of convergence as well as asymptotic normality are obtained, including for the density and its successive derivatives. Simulations appear and are commented. The starting point of the third chapter is the Parzen-Rosenblatt estimator (Rosenblatt (1956), Parzen (1964)) of the density. We first improve the bias of the Parzen-Rosenblatt estimator and its successive derivatives using higher order kernels (Berlinet (1993)). We then prove the new asymptotic normality conditions of these estimators. Finally, we construct an edge effect correction method for estimators of density derivatives using higher order derivatives. The last chapter focuses on the hazard rate, which unlike the two distribution functionals treated in the first chapter, is not a ratio of two linear distribution functionals. In the i.i.d. framework, the kernel estimators of the hazard rate and its successive derivatives are constructed from the kernel estimators of the density and its successive derivatives. The asymptotic normality of the first estimators is logically obtained from that of the second. We then place ourselves in the multiplicative intensity model, a more general framework encompassing censored and dependent data. We conduct the Ramlau-Hansen (1983) forward procedure to obtain good asymptotic properties of the estimators of the hazard rate and its successive derivatives and then attempt to apply the local polynomial approximation in this context. The rate of accumulation of surplus in the area of profit sharing can then be estimated nonparametrically since it depends on the transition rates (hazard rate from one state to another) of a Markov chain (Ramlau-Hansen (1991), Norberg (1999)).

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This paper investigates the notion of changes in ambiguity over loss probabilities in the smooth ambiguity model developed by Klibanoff, Marinacci and Mukerji (2005). Changes in ambiguity over loss probabilities are expressed through the specific concept of stochastic dominance of order n defined by Ekern (1980). We characterize conditions on the function capturing attitudes towards ambiguity under which an individual always considers one situation to be more ambiguous than another in a model of two states of nature. We propose an intuitive interpretation of the properties of this function in terms of preferences for harms disaggregation over probabilities, also labelled ambiguity apportionment.

This paper investigates the notion of treatment threshold for preventive treatment with potential side effects in the context of changes in risk. Changes in risk are defined by the concept of nth-order stochastic dominance and concern the effectiveness of preventive treatment, side effects, severity of the potential disease, and comorbidity risk. The impact of a riskier environment on the probability of disease threshold above which the preferable decision is to undergo preventive treatment is shown to depend on both mixed risk averse individual preferences and the configuration of increase in risk considered. These results suggest that neglecting differences between risks when evaluating the treatment threshold is likely to lead to substantial errors in most cost-benefit applications for preventive treatment. Copyright © 2014 John Wiley & Sons, Ltd.