Joint law of an Ornstein–Uhlenbeck process and its supremum. (June 2020) - Blanchet-Scalliet, Christophette; Dorobantu, Diana; Gay, Laura
Abstract: Let X be an Ornstein–Uhlenbeck process driven by a Brownian motion. We propose an expression for the joint density / distribution function of the process and its running supremum. This law is expressed as an expansion involving parabolic cylinder functions. Numerically, we obtain this law faster with our expression than with a Monte Carlo method. Numerical applications illustrate the interest of this result.