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...

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...

This paper is the sequel of Part I [1], where we showed how to use the so-called Malliavin calculus in order to devise efficient Monte-Carlo (numerical) methods for Finance. First, we return to the formulas developed in [1] concerning the "greeks" used in European options, and we answer to the...

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 integration-by-parts formula, which lies at the core of the theory of variational stochastic calculus, as developed in the Malliavin...

The sophistication of financial decisions varies with age: middle-aged adults borrow at lower interest rates and pay fewer fees compared to both younger and older adults. We document this pattern in ten financial markets. The measured effects cannot be explained by observed risk characteristics....

We measure learning and forgetting dynamics using a panel with four million monthly credit card statements. Through negative feedback -- i.e. paying a fee -- consumers learn to avoid future fees. Paying a fee last month reduces fee payment in the current month by 40%. Monthly fee payments fall...

We present a theory of excess stock market volatility, in which market movements are due to trades by very large institutional investors in relatively illiquid markets. Such trades generate significant spikes in returns and volume, even in the absence of important news about fundamentals. We...

A power law is the form taken by a large number of surprising empirical regularities in economics and finance. This article surveys well-documented empirical power laws concerning income and wealth, the size of cities and firms, stock market returns, trading volume, international trade, and...