An interval of no-arbitrage prices in financial markets with volatility uncertainty (Q1992892)

Summary: In financial markets with volatility uncertainty, we assume that their risks are caused by uncertain volatilities and their assets are effectively allocated in the risk-free asset and a risky stock, whose price process is supposed to follow a geometric \(G\)-Brownian motion rather than a classical Brownian motion. The concept of arbitrage is used to deal with this complex situation and we consider stock price dynamics with no-arbitrage opportunities. For general European contingent claims, we deduce the interval of no-arbitrage price and the clear results are derived in the Markovian case.