Capture Basin Algorithm for Evaluating and Managing Complex Financial Instruments

One aim of Viability Theory is to regulate evolutions under uncertainty in order not only to reach a target in finite time, but also to fulfill constraints (known as viability) until this time. Within the framework of finance, in the case of replicating portfolios, the target is defined by the payoff function at maturity time, and the constraints appear when one want to take into account limitations on prices and quantities to share. Moreover, extension of Viability Theory to hybrid or impulse systems allows to evaluate more complex financial instruments.