The Randomized American Option as a Classical Solution to the Penalized Problem - Guillaume Leduc (Journal of Function Spaces)
We connect the exercisability randomized American option to the penalty method by showing that the randomized American option value u is the unique classical solution to the Cauchy problem corresponding to the canonical penalty problem for American options. We also establish a uniform bound for Au, where A is the infinitesimal generator of a geometric Brownian motion.