The solution of the Kolmogorov backward equation is expressed as a functional integral by means of the Feynman–Kac formula. The expectation value is approximated as a mean over trajectories. In order to reduce the variance of the estimate, importance sampling is utilized. From the optimal...

Recent research suggests that fractional Brownian motion can be used to model the long-range dependence structure of the stock market. Fractional Brownian motion is not a semi-martingale and arbitrage opportunities do exist, however. Hu and Øksendal [Infin. Dimens. Anal., Quant. Probab. Relat....

We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time τ⩾0. This is accomplished by assuming that the underlying noise in the system is derived by an Ornstein-Uhlenbeck, rather than from a...