No abstract

No abstract

No abstract

A player starts at s in (0,1) and tries to reach 1. The process {Xt• t l OJ of his positions moves according to a diffusion process (or, more generally, an Ito process) whose infinitesimal parameters p,o are chosen by the player at each instant of time from a set depending on his current po1ition. To maximize the probability of reaching 1, the player should ohoose the parameters so 2 as to maximize p/o, at least when the maximum i1 achieved by bouded, measurable functions. This implies that bold (timid) play la optimal for subfair (superfalr), continuous-time red-and-black. Furthermore, in superfair red-and-black, tho strategy which maximizes the drift coefficient of (log Xt) minimizes the expected time to reach 1 • Key worda: Stochastic control, sambling theory, Red-and-Black.

No abstract