Lookback options are path dependent contingent claims whose payoffs depend on the extrema of a given security's price over a certain period of time. Using probabilistic tools, the authors derive explicit formulas for various European lookback options and provide some results about their American...

This paper presents an original probabilistic method for the numerical computations of Greeks (i.e. price sensitivities) in finance. Our approach is based on the {\it integration-by-parts} formula, which lies at the core of the theory of variational stochastic calculus, as developed in the...

In spite of the growing consideration for optimal execution in the financial mathematics literature, numerical approximations of optimal trading curves are almost never discussed. In this article, we present a numerical method to approximate the optimal strategy of a trader willing to unwind a...

This article discusses the discount rate to be used in projects that aimed at improving the environment. The model has two different goods, one is the usual consumption good whose production may increase exponentially, the other is an environmental good whose quality remains limited. The...

This article discusses the discount rate to be used in projects that aimed at improving the environment. The model is quite stylized and involves two different goods, one is the usual consumption good whose production increases exponentially, the other is an environmental good whose quality...

The article titled "Autour des taux écologiques" is a study of an economic environment in which individuals don’t care only about their intertemporal flow of consumption but also about the quality of a given natural resource, say air or water, denoted hereafter environmental good.

This paper deals with a stochastic order-driven market model with waiting costs, for order books with heterogenous traders. Offer and demand of liquidity drives price formation and traders anticipate future evolutions of the order book. The natural framework we use is mean field game theory, a...