Uncertainty and Probability PDE Approach: Modified Hamilton–Jacobi–Bellman Equation

PDE Approach: A Modified HJB Equation

Theorem (Verification Theorem)

Let v be a viscosity solution of the g –HJB equation

max{f(x)−v(t,x),vt(t,x) +Lv(t,x) +g(t,vx(t,x)σ(x))} = 0. (3)

Then Vt=v(t,St).

nonlinearity only in the first–order term

numeric analysis feasible

ambiguity introduces an additional nonlinear drift term