Treatment of the apparently whimsical fluctuations of the stock quotations as truly non stationary processes requires a model of such complexity that its practical value is likely to be limited. An additional complication, not encompassed by most stock market models, arises from the manifestation of the market as a nonzero sum game.
Richard Arnold EpsteinWhile no rigorous proof of an optimal strategy has been achieved, Robbins has proposed the principal of "staying on a winner" and has shown it to be uniformly better than a strategy of random selection.
Richard Arnold EpsteinThe essence of the phenomenon of gambling is decision making. The act of making a decision consists of selecting one course of action, or strategy, from among the set of admissible strategies.
Richard Arnold EpsteinGenerally, a betting system for which each wager depends only on present resources and present probability of success is known as a Markov betting system.
Richard Arnold EpsteinFrom a rational standpoint, it might be expected that man should be far more willing to express financial confidence in his skills rather than risking his earnings on the mindless meanderings of chance. Experience, however, has strongly indicated the reverse proposition to hold true.
Richard Arnold Epstein