The CEV model and its application to financial markets with volatility uncertainty

We survey the financial markets whose risks are caused by uncertain volatilities. The financial markets focus on the assets which are effectively allocated in one risk-free asset and one risky asset, whose price process is governed by the constant elasticity of variance (CEV for short) model which contains the G-Brownian motion rather than the classical Brownian motion. Such the CEV model which includes the G-Brownian motion utilized to financial markets is the extension of the classical CEV model. Applying the concept of arbitrage and the properties of G-expectation, we consider stock price dynamics which exclude arbitrage opportunities. Moreover, the interval of no-arbitrage price for the general European contingent claims is found in the Markovian case.