2007 Spring School  
Viability: Models, Algorithms and Applications
in Finance and EnvironmentalEconomics 

April 1620, 2007  


Registration Speakers Venue Schedule Links Accommodation Contact Poster Online information Organised by: Michèle Breton, CREF, GERAD, HEC Montréal
Georges Zaccour, Chair in game theory and
management, Sponsors: Centre for Research on efinance (CREF) Chair in game theory and management 
The aim of this tutorial is to explain how the mathematical and algorithmic tools of viability theory can be used to solve some issues in both mathematical finance and environmental studies. In a nutshell, viability theory investigates evolutions
in continuous time, discrete time, or an "hybrid" of the two when impulses are involved,
constrained to adapt to an environment,
evolving under contingent, stochastic or tychastic uncertainty,
using for this purpose controls, regulons (regulation controls), subsets of regulons, and in the case of networks, connectionist matrices,
regulated by feedback laws (static or dynamic) that are then "computed" according to given principles, such as the inertia principle, intertemporal optimization, etc.,
coevolving with their environment (mutational and morphological viability),
and corrected by introducing adequate controls (viability multipliers) when viability or capturability is at stakes.
Main concepts and examples: Viability Kernels of an environment and Capture Basins of a target viable in an environment. Viable Feedbacks. Examples. Viability Algorithms (principle). Cascade of environments. Chaining of feedbacks and concatenation of environments. Tychastic uncertainty. Comparison between stochastic and tychastic viability kernels
Environmental Applications: Inertia Function, dynamic of renewable resources, fisheries, heavy and cyclic evolutions, control of Green House Gases,
Mathematical finance: Viability formulation of the pricing and management of portfolios and cash flows, applications to options, implicit volatility
New perspectives: viability multipliers, impulse systems and mutational equations
Back to mathematics: Viability and Invariance Theorems, HamiltonJacobi equations and other issues.
Lecture notes and executables of software will be provided and flexibility is planned to answer questions of interest by the participants (closedloop pedagogy).