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

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...

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...