In this note, we prove that under some minor conditions on $\sigma$, if a martingale $X_t = \int_0^t \sigma_u dW_u $ satisfies, for every given pair $u \geq 0, \, \xi \geq 0$, $X_{u+\xi}-X_u{\mathop{=}^{\mathrm{(law)}}} X_{\xi},$ then necessarily, $|\sigma_u|$ is a constant and X is a constant...

This paper considers investors who are looking to maximize their probability of remaining solvent throughout their lifetime by using an algorithm that aims to optimize their investment allocation strategy and optimize their tax strategy for withdrawal allocations between tax deferred accounts...

This paper is the sequel of Part I [1], where we showed how to use the so-called Malliavin calculus in order to devise efficient Monte-Carlo (numerical) methods for Finance. First, we return to the formulas developed in [1] concerning the "greeks" used in European options, and we answer to the...