# Publications

Household surveys do not capture incomes at the top of the distribution well. This yields biased inequality measures. We compare the performance of the reweighting and replacing methods to address top incomes underreporting in surveys using information from tax records. The biggest challenge is that the true threshold above which underreporting occurs is unknown. Relying on simulation, we construct a hypothetical true distribution and a “distorted” distribution that mimics an underreporting pattern found in a novel linked data for Uruguay. Our simulations show that if one chooses a threshold that is not close to the true one, corrected inequality measures may be significantly biased. Interestingly, the bias using the replacing method is less sensitive to the choice of threshold. We approach the threshold selection challenge in practice using the Uruguayan linked data. Our findings are analogous to the simulation exercise. These results, however, should not be considered a general assessment of the two methods.

I present a model of optimal capital taxation where agents with heterogeneous labor productivity randomly draw their rate of return to savings. Because of scale dependence, the distribution of rates of returns can depend on the amount saved. Uncertainty in returns to savings yields an insurance rationale for taxing capital on top of labor income. I first show that, because of scale dependence, agents making the same saving decision should access the same rate of return at the optimum. I then constrain the information set of the government and show that, as soon as return are uncertain, positive capital income taxation is needed at the optimum. The optimal linear tax on capital income trades off insurance with distortions to both savings and to the rate of return in a context of scale dependence. Eventually, I argue that scale dependence in and of itself is not sufficient to justify capital taxation on top of labor income taxes. These results are still valid when agents can optimize between a risk-free and a risky-asset that can both exhibit scale dependence.

We propose an inertial proximal point method for variational inclusion involving difference of two maximal monotone vector fields in Hadamard manifolds. We prove that if the sequence generated by the method is bounded, then every cluster point is a solution of the non-monotone variational inclusion. Some sufficient conditions for boundedness and full convergence of the sequence are presented. The efficiency of the method is verified by numerical experiments comparing its performance with classical versions of the method for monotone and non-monotone problems.

We study repeated zero-sum games where one of the players pays a certain cost each time he changes his action. We derive the properties of the value and optimal strategies as a function of the ratio between the switching costs and the stage payoffs. In particular, the strategies exhibit a robustness property and typically do not change with a small perturbation of this ratio. Our analysis extends partially to the case where the players are limited to simpler strategies that are history independent―namely, static strategies. In this case, we also characterize the (minimax) value and the strategies for obtaining it.

We formulate a hydro-economic model of the North-Western Sahara Aquifer System (NWSAS) to assess the effects of intensive pumping on the groundwater stock and examine the subsequent consequences of aquifer depletion. This large system comprises multi-layer reservoirs with vertical exchanges, all exploited under open access properties. We first develop a theoretical model to account for relevant features of the NWSAS by introducing, in the standard Gisser-Sanchez model, a non-stationary demand and quadratic stock-dependent cost functions. In the second step, we calibrate parameters values using data from the NWSAS over 1955–2000. We finally simulate the time evolution of the aquifer system with exploitation under an open-access regime. We specifically examine time trajectories of the piezometric levels in the two reservoirs, the natural outlets, and the modification of water balances. We find that natural outlets of the two reservoirs might be totally dried before 2050.

We first give a pre-order principle whose form is very general. Combining the pre-order principle and generalized Gerstewitz functions, we establish a general equilibrium version of set-valued Ekeland variational principle (denoted by EVP), where the objective function is a set-valued bimap defined on the product of quasi-metric spaces and taking values in a quasi-ordered linear space, and the perturbation consists of a subset of the ordering cone multiplied by the quasi-metric. From this, we obtain a number of new results which essentially improve the related results. Particularly, the earlier lower boundedness condition has been weakened. Finally, we apply the new EVPs to Psychology.

We investigate whether and how an individual giving decision is affected in risky environments in which the recipient’s wealth is random. We demonstrate that, under risk neutrality, the donation of dictators with a purely ex post view of fairness should, in general, be affected by the riskiness of the recipient’s payoff, while dictators with a purely ex ante view should not be. Furthermore, we observe that some influential inequality aversion preferences functions yield opposite predictions when we consider ex post view of fairness. Hence, we report on dictator games laboratory experiments in which the recipient’s wealth is exposed to an actuarially neutral and additive background risk. Our experimental data show no statistically significant impact of the recipient’s risk exposure on dictators’ giving decisions. This result appears robust to both the experimental design (within subjects or between subjects) and the origin of the recipient’s risk exposure (chosen by the recipient or imposed on the recipient). Although we cannot sharply validate or invalidate alternative fairness theories, the whole pattern of our experimental data can be simply explained by assuming ex ante view of fairness and risk neutrality.

We study price personalization in a two period duopoly with horizontally differentiated products. In the second period, a firm has collected detailed information on its old customers, using it to engage in price personalization. Customers, when returning to buy, may choose to incur a cost in order to access the standard offer of their previous provider in addition to its personalized offer and the standard offer of its rival. The analysis confirms that firms’ second period profits are boosted when consumers are active in this sense (being equal to perfect price discrimination ones when initial market hares do not differ too much) but it reveals that this advantage is dissipated and possibly over-dissipated by the resulting fierce first-period competition for the market. Two-period aggregate profits are smaller with active customers provided the consumers are naive and/or the firms patient enough. Consumers’ access to both personalized and standard firms’ offers which benefit the oligopolists in mature markets may plausibly hurt them in emergent ones. The equilibrium is shown not to depend on the level of the cost as long as it is below some critical value.

We present an inexact proximal point algorithm using quasi distances to solve a minimization problem in the Euclidean space. This algorithm is motivated by the proximal methods introduced by Attouch et al., section 4, (Math Program Ser A, 137: 91–129, 2013) and Solodov and Svaiter (Set Valued Anal 7:323–345, 1999). In contrast, in this paper we consider quasi distances, arbitrary (non necessary smooth) objective functions, scalar errors in each objective regularized approximation and vectorial errors on the residual of the regularized critical point, that is, we have an error on the optimality condition of the proximal subproblem at the new point. We obtain, under a coercivity assumption of the objective function, that all accumulation points of the sequence generated by the algorithm are critical points (minimizer points in the convex case) of the minimization problem. As an application we consider a human location problem: How to travel around the world and prepare the trip of a lifetime.

The objective of this paper is to emphasize the differences between a call and a warrant as well as the different valuation methods of warrants which have been introduced in the financial literature. For the sake of simplicity and applicability, we only consider a debt-free equity-financed firm. More recently a formal distinction between structural and reduced form pricing models has been introduced. This distinction is important whether one wishes to price a new warrant issue or outstanding warrants. If we are interested in pricing a new issue of warrants, e.g. in the context of a management incentive package, one has to rely on a structural model. However most of practitioners use the simple Black-Scholes formula. In this context, we analyze the accuracy of the approximation of the “true” price of a warrant by the Black-Scholes formula. We show that in the current low interest rate environment, the quality of the approximation deteriorates and the sensitivity of this approximation to the volatility estimate increases.