The Hybrid Guaranteed Capture Basin Algorithm in Economics

Reaching a target while remaining in a given set for impulse dynamics can be characterized by a non deterministic controlled differential equation and a controlled instantaneous reset equation. The set of initial conditions from which a given objective can be reached is calculated using the Hybrid Guaranteed Capture Basin Algorithm. This algorithm was developed in finance to evaluate options in absence of impulse but in the presence of uncertainty and in control to evaluate minimal time functions to reach a target, in the presence of impulse but in absence of uncertainty. We study the problem of reaching a target in the presence of both impulse and uncertainty and present two applications in economics.