Pathwise Dynamic Programming For A Regime-Switching Uncertain Volatility Model Of European Option

This artic-le mainly concentrates on the stochastic differential equation which is de.rived from the European option under uncertain volatility,which is regime-switching.First,we introduce the background of regime-switching model for European option.Then we derive the Hamilton-Jacobi-Bellman equation from the initial stochastic differential equation.Tirme discretization schemes will be in use and the discrete form is a convex-concave structure.Finally,a pathwise recursion formula will be given.