A Dynamic Equilibrium Model of Real Exchange Rates with General Transaction Costs

We study the behavior of real exchange rates in a two­country dynamic equilibrium model. In this model, consumers can only consume domestic goods but can invest costlessly in capital stocks of both countries. Nevertheless, transporting goods between the two countries is costly and, hence, the rebalancing of the capital stock can only happen finitely often. We propose a realistic cost structure for goods transportation, wherein the total cost increases with the amount of shipment but the unit cost decreases with it due to economies of scale. Given such a cost structure, the optimal decisions on when and how much to transfer need to be determined jointly. The dual decision depends upon the magnitude of economies of scale, the production technology specifications, and the consumer preferences. The model can reconcile the observed large short­term volatility of the real exchange rate with its slow convergence to parity. Further, the drift and diffusion of the real exchange rate are not uniquely determined by the real exchange rate level. The dynamics of the real exchange rate can only be determined by a joint analysis of the real exchange rate and the underlying economic fundamentals such as the capital stock imbalance between the two countries.costs of goods transportation; economies of scale; real exchange rate; purchasing power parity; nonlinearity.

Optimal Trading Strategy and Supply/Demand Dynamics

The supply/demand of a security in the market is an intertemporal, not a static, object and its dynamics is crucial in determining market participants' trading behavior. Previous studies on the optimal trading strategy to execute a given order focuses mostly on the static properties of the supply/demand. In this paper, we show that the dynamics of the supply/demand is of critical importance to the optimal execution strategy, especially when trading times are endogenously chosen. Using a limit-order-book market, we develop a simple framework to model the dynamics of supply/demand and its impact on execution cost. We show that the optimal execution strategy involves both discrete and continuous trades, not only continuous trades as previous work suggested. The cost savings from the optimal strategy over the simple continuous strategy can be substantial. We also show that the predictions about the optimal trading behavior can have interesting implications on the observed behavior of intraday volume, volatility and prices.

Investissement, produits financiers et anomalies boursières

Understanding and explaining the risk-return relationship is considered as a main issue in finance. Since the mean-variance model, the investment decision for both investors and firms is based on an optimization of risk and return. Nevertheless, the observation of anomalies in financial markets, the succession of financial crises and the growing interest to the extra-financial rating require broadening the spectrum analysis of this relationship. In our research work, we shed light on the investment decision for three assets (equities, bonds and derivatives). First, we study asset pricing models and especially the three-factor Fama and French (1993) model in explaining value and size premiums on the French stock market. We show that factor models fit better excess return description. Then, we revisit the duration-convexity approximation used in hedging bond positions. We propose an approximation that leads to a perfect fit of the bond change. For derivatives, we identify the determinants of hedging derivatives decision in the case of French companies. Dealing with the portfolio selection and optimization problem in the point of view of individual investors, we give the number of securities providing the maximum return in the presence of transaction costs. Finally, we introduce the regulatory and institutional framework in understanding the risk-return relationship. Three important issues are considered: the responsibility or not of market discipline in the transformation of the relationship risk-return during the financial crisis, the responsibility of Environmental, Social and Governance (ESG) criteria in redefining the investment decision in the French regulatory framework of Grenelle 2 law, and corporate social responsibility measured by the extra-financial rating and its dependence on institutional and legal framework.La relation linéaire entre la rentabilité et le risque qui date des travaux de Markowitz (1952) constitue un axe central de recherche en finance. Depuis sa formalisation dans le cadre du modèle moyenne-variance, la décision d’investissement aussi bien pour l’investisseur que l’entreprise repose sur un raisonnement d’optimisation de la rentabilité et du risque. Néanmoins, l’observation des anomalies sur les marchés financiers, la succession des crises financières et l’intérêt croissant porté à la notation extra-financière des entreprises élargissent le spectre d’analyse de cette relation. Ma réflexion entre dans ce cadre spécifique couvrant ainsi plusieurs champs de la recherche en finance. Le premier axe de réflexion analyse la relation rentabilité-risque dans le cadre du marché français des actions. La problématique générale posée porte sur la légitimité des modèles ad hoc comme celui à trois facteurs de Fama et French (1993) dans l’explication des anomalies. A ce titre quatre essais sur le modèle à trois facteurs sont menés. Les résultats suggèrent la supériorité de ce dernier modèle dans l’explication des rentabilités des titres français. Le deuxième thème de recherche s’intéresse aux obligations. Plus spécifiquement, le couple rentabilité-risque est analysé dans le cas d’une obligation suite à une variation de la structure par termes des taux d’intérêts. Un développement théorique démontre les limites de l’approximation de la variation du prix d’une obligation donnée dans la littérature financière et une solution explicite et précise est présentée. Dans le troisième axe de recherche, le couple rentabilité-risque est considéré dans le cadre des produits dérivés. Plus précisément, les déterminants de la décision de couverture des risques par des produits dérivés dans le cas des entreprises françaises sont identifiés. Le quatrième axe de recherche considère la relation rentabilité-risque dans le cas d’un investisseur individuel en intégrant les coûts de transactions. Ces derniers sont soit ignorés, soit traités d’une manière sommaire éloignée de la pratique par la littérature financière. Une solution analytique au problème d’optimisation de l’investisseur donnant le nombre d’actifs à acheter maximisant son rendement en présence d’une fonction par paliers des couts de transaction est présentée. Ce développement théorique est corroboré par des simulations numériques proches de la pratique. Enfin, le cinquième thème introduit une approche plus globale du couple rentabilité-risque intégrant le cadre règlementaire et institutionnel. Trois réflexions sont exposées : la responsabilité ou non de la discipline de marché dans la transformation de la relation rentabilité-risque au cours des crises financières, la responsabilité des critères Environnementaux, Sociaux et de Gouvernance (ESG) dans la redéfinition de la décision d’investissement avec le cadre règlementaire français de la loi Grenelle 2, et la responsabilité sociétale des entreprises mesurée par la notation extra-financière et sa dépendance au cadre institutionnel et juridique

A Differential Game Control Problem in Finite Horizon with an Application to Portfolio Optimization

This paper considers a new class of deterministic finite-time horizon, two-player, zero-sum differential games (DGs) in which the maximizing player is allowed to take continuous and impulse controls whereas the minimizing player is allowed to take impulse control only. We seek to approximate the value function, and to provide a verification theorem for this class of DGs. We first, by means of dynamic programming principle (DPP) in viscosity solution (VS) framework, characterize the value function as the unique VS to the related Hamilton-Jacobi-Bellman-Isaacs (HJBI) double-obstacle equation. Next, we prove that an approximate value function exists, that it is the unique solution to an approximate HJBI double-obstacle equation, and converges locally uniformly towards the value function of each player when the time discretization step goes to zero. Moreover, we provide a verification theorem which characterizes a Nash-equilibrium for the DG control problem considered. Finally, by applying our results, we derive a new continuous-time portfolio optimization model, and we provide related computational algorithms.Comment: 38 page

A fixed-point policy-iteration-type algorithm for symmetric nonzero-sum stochastic impulse control games

Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has hindered their proliferation. Semi-analytical approaches make strong assumptions pertaining to very particular cases. To the author’s best knowledge, the only numerical method in the literature is the heuristic one we put forward in Aïd et al (ESAIM Proc Surv 65:27–45, 2019) to solve an underlying system of quasi-variational inequalities. Focusing on symmetric games, this paper presents a simpler, more precise and efficient fixed-point policy-iteration-type algorithm which removes the strong dependence on the initial guess and the relaxation scheme of the previous method. A rigorous convergence analysis is undertaken with natural assumptions on the players strategies, which admit graph-theoretic interpretations in the context of weakly chained diagonally dominant matrices. A novel provably convergent single-player impulse control solver is also provided. The main algorithm is used to compute with high precision equilibrium payoffs and Nash equilibria of otherwise very challenging problems, and even some which go beyond the scope of the currently available theory