This study reconsiders the problem of hedging a liability by a portfolio made of a riskless asset and an underlying (underlying).

This paper deals with inertia functions in control theory introduced in Aubin, Bernardo and Saint-Pierre (2004, 2005) and their adaptation to dynamical games. The inertia function associates with any initial state-control pair the smallest of the worst norms over time of the velocities of the...

This paper examines a decentralized, dynamical, pure exchange economy in which changes in an individual consumers demand depend on his own consumption and on prices. An ‘instantaneous Walras law’ provides a sufficient condition for the existence of viable exchange trajectories. Such dynamic...

We use in this chapter the viability/capturability approach for studying the problem of dynamic valuation and management of a portfolio with transaction costs in the framework of tychastic control systems (or dynamical games against nature) instead of stochastic control systems. Indeed, the very...

Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion "Samuelson" market model (also known as the Black-Scholes model because it is used in that most...