Duality for pathwise superhedging in continuous time

Finance and Stochastics - We provide a model-free pricing–hedging duality in continuous time. For a frictionless market consisting of $d$  risky assets with continuous price...     

Machine learning for pricing American options in high-dimensional Markovian and non-Markovian models

In this paper we propose two efficient techniques which allow one to compute the price of American basket options. In particular, we consider a basket of assets that follow a multi-dimensional Black–Scholes dynamics. The proposed techniques, called GPR Tree (GRP-Tree) and GPR Exact Integration (GPR-EI), are both based on Machine Learning, exploited together with binomial trees or with a closed form formula for integration. Moreover, these two methods solve the backward dynamic programing problem considering a Bermudan approximation of the American option. On the exercise dates, the value of the option is first computed as the maximum between the exercise value and the continuation value and then approximated by means of Gaussian Process Regression. The two methods mainly differ in the approach used to compute the continuation value: a single step of the binomial tree or integration according to the probability density of the process. Numerical results show that these two methods are accurate and reliable in handling American options on very large baskets of assets. Moreover we also consider the rough Bergomi model, which provides stochastic volatility with memory. Despite that this model is only bidimensional, the whole history of the process impacts on the price, and how to handle all this information is not obvious at all. To this aim, we present how to adapt the GPR-Tree and GPR-EI methods and we focus on pricing American options in this non-Markovian framework.     

A GENERALIZED OLIGOPOLY MODEL WITH CONJECTURAL VARIATIONS

This paper considers a generalization of the Stackelberg model to cover a T‐stage framework with several leaders and followers who compete on quantities. Assuming a linear demand function and constant marginal costs, we introduce constant conjectural variations in order to capture various structures of competition. First, we characterize the equilibrium market outcome. Second, we study the influence of conjectures on welfare. We notably propose a welfare comparison for six symmetric equilibria. Third, we consider convergence analysis, and we also show that the competitive equilibrium is a consistent oligopoly equilibrium.     

Gaussian process regression for pricing variable annuities with stochastic volatility and interest rate

Decisions in Economics and Finance - In this paper, we investigate value and Greeks computation of a guaranteed minimum withdrawal benefit (GMWB) variable annuity, when both stochastic volatility...     

Conjectural variations, symmetric equilibria and economic policy

In this paper, we consider conjectural variations in a simple static general equilibrium model under oligopolistic competition. The modeling of conjectures captures the role played by beliefs in a micro-founded model. So, the economy may have three kinds of symmetric general equilibria. Furthermore, these equilibria can be Pareto-ranked by the conjectural variation parameter. Finally, we consider the implementation of a tax on the strategic behaviors in case of balanced-budget rule. The comparative statics illustrates the idea according to which the effectiveness of the multiplier mechanism to mitigate the market distortions depends on the symmetric equilibrium considered. Therefore, the effect of the tax on the prices and economic activity depends on the degree of market power which is conjectured by the agents.     

Applying mathematics to economics according to Cournot and Walras

This article examines the reasons that led Cournot to refuse Walras's request that he writes an article defending mathematical economics. From a reading of Cournot's works on philosophy and economics we show three reasons which explain the Cournot's refusal. First, Cournot does not attach the same importance to the theorems proposed by Walras. Second, these theorems enable Walras to defend an economic system that he considers to be truer than any other while Cournot believed that the economy could be subject to various forms of mathematical representations. Third, Cournot does not refer to the same conception of mathematics of Walras.     

A note on Stackelberg competition

This note investigates a Stackelberg–Nash competition model. We determine the conditions under which the leaders may achieve better profits than the followers when all firms compete on quantity in a two stage game. We focus on the properties of the followers’ best response functions. It is shown that the Stackelberg equilibrium may coincide with the Cournot equilibrium. In addition, the followers may achieve higher profits than the leaders. Such results put forward the working and the consequences of strategic complementarities. These results are illustrated with three examples.     

Participatory determinants of innovation and their impact on plantain production systems in Cameroon

Current statistics question the capacity of food-crop production to meet the challenges of food security in Central Africa. However, for local food crops like plantain, the potential for improving productivity is very high. In response to this challenge, after identification of the most serious constraints, an interdisciplinary team used participatory research and action-research tools to try and speed up the adoption of technical innovation by farmers. The project began in 1990 in South-West Province and subsequently expanded to include 100 plantain producers and 60 extension technicians in the Central and Southern Provinces of Cameroon. The approach used produced satisfactory results as far as the adoption and dissemination of methods of multiplication and cleaning of planting material were concerned but there was resistance to new cropping practices involving intercrops and crop rotation. The project resulted in major technical changes in plantain production systems in Cameroon that not only increased productivity and food security but also reduced deforestation showing that sustainable intensification is possible in sub-Saharan Africa.     

Pollution in strategic multilateral exchange: Taxing emissions or trading on permit markets?

We introduce polluting emissions in a sequential noncooperative oligopoly model of bilateral exchange. In one sector, a leader and a follower use polluting technologies which create negative externalities on the payoffs of strategic traders who belong to the other sector. By modeling emissions as a negative externality, we show that the leader pollutes more (less) than the follower when strategies are substitutes (complements). Then, we consider the implementation of public policies to control the levels of emissions, namely, two taxation mechanisms and a permit market. We study the effects of these public policies. Moreover, we determine the conditions under which these public policies can implement a Pareto-improving allocation.