2007 Spring School
Viability: Models, Algorithms and Applications
in Finance and Environmental-Economics
April 16-20, 2007

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Organised by:

Michèle Breton, CREF, GERAD, HEC Montréal

Georges Zaccour, Chair in game theory and management,
HEC Montréal


Centre for Research on e-finance (CREF)

Chair in game theory and management

Group for Research in Decision Analysis (GERAD)


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

Topics Covered

  1. 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

  2. Environmental Applications: Inertia Function, dynamic of renewable resources, fisheries, heavy and cyclic evolutions, control of Green House Gases,

  3. Mathematical finance: Viability formulation of the pricing and management of portfolios and cash flows, applications to options, implicit volatility

  4. New perspectives: viability multipliers, impulse systems and mutational equations

  5. Back to mathematics: Viability and Invariance Theorems, Hamilton-Jacobi 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 (closed-loop pedagogy).