Universal strategies for diffusion markets and possibility of asymptotic arbitrage

The paper investigates the investment problem in a generic diffusion stochastic market model. Volatilities and appreciation rates are allowed to be random and unknown, with unknown prior distributions. We study “universal” strategies that use price observation only and do not require any knowledge on prior distributions of market parameters, i.e., where market parameters are not available. We define bounded risk strategies in this class that ensure a positive average gain for all random volatilities and appreciation rates from a wide class. Moreover, the strategies ensure a strengthened form of asymptotic arbitrage as the diversification of the portfolio increases: a given positive gain is ensured with probability arbitrarily close to 1.