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...

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...

We investigate the dynamic effect that the Tandroy's unsustainable practices have on the forest. The Tandroy people live in Androy, a region located in the southern part of Madagascar. They are mainly an agricultural and cattle herding society whose subsistence relies on the slash-and-burn...

We adopt viability theory to assess the sustainability of the world’s forests while taking into account some of the competing economic, social, and environmental uses of these forests, namely, timber production, poverty alleviation through agriculture, and air quality as well as the negative...

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

This paper presents an example of the advantages of using mathematical viability theory concepts and tools to study sustainable development issues. Instead of seeking optimal solutions according to a predefined value function, viability theory follows a inverse approach and does not postulate...

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...

A viability algorithm is developed to compute the constrained minimum time function for general dynamical systems. The algorithm is instantiated for a specific dynamics(Dubin’s vehicle forced by a flow field) in order to numerically solve the minimum time problem. With the specific...

We apply set valued analysis techniques in order to characterize the input-to-state dynamical stability (ISDS) property, a variant of the well known input-to-state stability (ISS) property. Using a suitable augmented differential inclusion we are able to characterize the epigraphs of minimal...