Optimal Risk Sharing for Law Invariant Monetary Utility Functions

We consider the problem of optimal risk sharing of some given total risk between two economic agents characterized by law-invariant monetary utility functions or equivalently, law-invariant risk measures. We first prove existence of an optimal risk sharing allocation which is in addition increasing in terms of the total risk. We next provide an explicit characterization in the case where both agents' utility functions are comonotone. The general form of the optimal contracts turns out to be given by a sum of options (stop-loss contracts, in the language of insurance) on the total risk. In order to show the robustness of this type of contracts to more general utility functions, we introduce a new notion of strict risk aversion conditionally on lower tail events, which is typically satisfied by the semi-deviation and the entropic risk measures. Then, in the context of an AV@R-agent facing an agent with strict monotone preferences and exhibiting strict risk aversion conditional on lower tail events, we prove that optimal contracts again are European options on the total risk.Monetary utility functions, comonotonicity, Pareto optimal allocations

Law Invariant Risk Measures Have the Fatou Property.

S. Kusuoka [K 01, Theorem 4] gave an interesting dual characterizationof law invariant coherent risk measures, satisfying the Fatou property.The latter property was introduced by F. Delbaen [D 02]. In thepresent note we extend Kusuoka's characterization in two directions, thefirst one being rather standard, while the second one is somewhat surprising. Firstly we generalize — similarly as M. Fritelli and E. Rossaza Gianin [FG05] — from the notion of coherent risk measures to the more general notion of convex risk measures as introduced by H. F¨ollmer and A. Schied [FS 04]. Secondly — and more importantly — we show that the hypothesis of Fatou property may actually be dropped as it is automatically implied by the hypothesis of law invariance.We also introduce the notion of the Lebesgue property of a convex risk measure, where the inequality in the definition of the Fatou property is replaced by an equality, and give some dual characterizations of this property.risk measures; Fatou property;

Law Invariant Risk Measures Have the Fatou Property

S. Kusuoka [K 01, Theorem 4] gave an interesting dual characterizationof law invariant coherent risk measures, satisfying the Fatou property.The latter property was introduced by F. Delbaen [D 02]. In thepresent note we extend Kusuoka's characterization in two directions, thefirst one being rather standard, while the second one is somewhat surprising. Firstly we generalize — similarly as M. Fritelli and E. Rossaza Gianin [FG05] — from the notion of coherent risk measures to the more general notion of convex risk measures as introduced by H. F¨ollmer and A. Schied [FS 04]. Secondly — and more importantly — we show that the hypothesis of Fatou property may actually be dropped as it is automatically implied by the hypothesis of law invariance.We also introduce the notion of the Lebesgue property of a convex risk measure, where the inequality in the definition of the Fatou property is replaced by an equality, and give some dual characterizations of this property.Fatou property, risk measures

Vector-valued Coherent Risk Measures

We define a coherent risk measures as set-valued maps satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner, Delbaen, Eber and Heath (1998). We then discuss the aggregation issue, i.e. the passage from valued random portofolio to valued measure of Risk. Necessary and sufficient conditions of coherent aggregation are providedrisk, measures

Optimal Investment with Taxes: An Existence Result

We study the deterministic control problem of maximizing utility from consumption of an agent who seeks to optimally allocate his wealth between consumption and investment in a FInancial asset subject to taxes on benefits with first-in-first-out priority rule on sales. Short sales are prohibitted and consumption is restricted to be non-negative. Such a problem has been introduced in a previous paper by the same authors where the first order conditions have been derived. In this paper, we establish an existence result for this non-classical optimal control problem

Optimal Investment with Taxes: An Existence Result

We study the deterministic control problem of maximizing utility from consumption of an agent who seeks to optimally allocate his wealth between consumption and investment in a financial asset subject to taxes on benefits with first-in-first-out priority rule on sales. Short-sales are prohibited and consumption is restricted to be nonnegative. Such a problem has been introduced in a previous paper by the same authors where the first order conditions have been derived. In this paper, we establish an existence result for this non-classical optimal control problem

North African countries (NACs) production and export structure: Towards diversification and export sophistication strategy

The North African countries (NACs) production and export structure is suffering from double constraints: insufficient diversification along with excessively weak sophistication. This study establish a deeper link between diversification/sophistication on and growth in the NACs. The study assesses the impact of these variables on the growth of these countries so as to verify whether the current export structure is indeed a constraint to the economic development. The approach used consists in estimating a growth model as a Barro's regression (conditional -convergence model) using panel data. The paper identify the factors determining diversification and sophistication of exports so as to find the various levers and actions which would firstly allow NACs to diversify their exports to higher added value products and secondly to take the existing products to a higher level of sophistication. The last part of this study proposes recommendations in terms of economic policies based on obtained results, highlighting the role of various stakeholders, and different policies

North African countries (NACs) production and export structure: Towards diversification and export sophistication strategy

The North African countries (NACs) production and export structure is suffering from double constraints: insufficient diversification along with excessively weak sophistication. This study establish a deeper link between diversification/sophistication on and growth in the NACs. The study assesses the impact of these variables on the growth of these countries so as to verify whether the current export structure is indeed a constraint to the economic development. The approach used consists in estimating a growth model as a Barro's regression (conditional -convergence model) using panel data. The paper identify the factors determining diversification and sophistication of exports so as to find the various levers and actions which would firstly allow NACs to diversify their exports to higher added value products and secondly to take the existing products to a higher level of sophistication. The last part of this study proposes recommendations in terms of economic policies based on obtained results, highlighting the role of various stakeholders, and different policies

Pas de titre en français

Cette thèse analyse les effets de la libéralisation du commerce des services en Tunisie. Le premier chapitre, étudie à l’aide d’un modèle DSGE, l'effet global de la libéralisation du secteur des services marchands sur la croissance économique tout en estimant les barrières à l'entrée que doivent supporter les investisseurs afin d’accéder à ce marché. Le deuxième chapitre analyse le cas particulier de la libéralisation du secteur bancaire ainsi que les effets sur l’accumulation du capital. En particulier, il suggère que l'accroissement de la concurrence via plus de libéralisation est bénéfique pour le secteur bancaire tunisien et permettra de doubler la quantité de capital réellement accumulé. Le troisième chapitre procède à l’estimation des effets direct et indirect de la libéralisation du transport aérien sur les flux de touristes dans les pays Méditerranéens. Les accords signés par ces pays seront considérés au même titre que ceux signés entre pays tiers. En effet, lorsque ces pays tiers disposent d'aéroports de transit par lesquels passent les touristes pour se rendre dans les pays de la Méditerranée, un accord de libéralisation les concernant peut ainsi être bénéfique aux derniers. Nous constituons une base originale pour tenir compte de tous ces accords. Nos résultats montrent que la libéralisation des secteurs de service en Tunisie a un effet positif et dépend essentiellement de la performance su secteur des biens et barrières à l'entrée, évalués à 37% de la production totale. En ce qui concerne le secteur bancaire tunisien, la libéralisation a un impact positif sur l'accumulation de capital pouvant aller jusqu'à 200% de l'accumulation actuelle. Enfin, l'étude de la libéralisation du transport aérien sur le tourisme montre qu'il y a une augmentation des flux de touristes utilisant des routes directes et indirectes. L'effet direct d'un accord (suite à l'accroissement d'une unité de l'indice de libéralisation) accroît de 3 à 4% les flux touristiques, tandis que l'effet indirect est compris entre 2% et 3%.This dissertation focuses on the effects of trade service liberalization in Tunisia. Using a DGSE model, the first chapter studies the overall effect of service liberalization on economic growth while considering the non-tariff barriers preventing investors to access this market. The second chapter analyzes the particular case of the banking sector liberalization by estimating its effect on capital accumulation. In particular, it suggests that increasing bank competition via liberalization is benefitting to the Tunisian banking sector up to a doubling of its capital accumulation. The third chapter shall estimate the direct and indirect effect of air transport liberalization on tourist flows in the southern Mediterranean countries. The agreements signed by these countries will be considered as well as those signed between third countries. In particular, when these third countries have transit airports through which pass tourists to visit Mediterrenean countries, liberalization can also be beneficial to the latter. For this purpose we have collected an original database to account for all of these agreements. Our results show that the liberalization of the service sector in Tunisia has a positive effect and depends mainly on the performance of the goods sector as well as the value of non-tariff barriers, evaluated at 37% of total of production. Morever, the liberalization of the Tunisian banking sector has a positive impact on capital accumulation running up to about 200 % of the current accumulation. Finally, the study of air transport liberalization on tourism shows that there is an increase in tourist flows using direct and indirect routes. The direct effect (following one unit increase of the liberalization index) increases the tourist flows by 3 to 4 percent, while the indirect effect is between 2 and 3 percent