## Asymptotic Arbitrage in a Stochastic Economic Model

### BibTeX

@MISC{Dokuchaev_asymptoticarbitrage,

author = {N.G. Dokuchaev and A.V. Savkin},

title = {Asymptotic Arbitrage in a Stochastic Economic Model},

year = {}

}

### OpenURL

### Abstract

The paper investigates the investment problem in a diffusion stochastic economic model with an infinitive number of commodities. Hedging investment strategies are proposed and investigated. These strategies do not require forecasting of the volatility coefficient and depend on the historical volatility only, and the volatility coefficient is estimated at current time. It is shown that these strategies converge to arbitrage as the number of the traded stocks increases. Hence it is an example of asymptotic arbitrage ("free lunch") without borrowing. Keywords: Portfolio choice, Diffusion market model, Historical volatility, Asymptotic arbitrage 1 Introduction The paper investigates the investment problem in a stochastic diffusion model of a securities market which consists of the risk free bond or bank account and infinite number of risky stocks. It is assumed that the dynamics of the stocks is given by random processes with some standard deviations of the stock returns (the volatility c...