On the expectation of the local time of the fractional Brownian motion

In this paper, we prove some new formulas of the expectations of L B H and L B H the local time and the weighted local time of B H the fractional Brownian motion with Hurst parameter H . These formulas are based on f the probability density function of N ( 0 , 1 ) the standard normal distribution and Γ the upper incomplete Gamma function. These expectations are useful in the evaluation of hedging errors and option prices in financial markets.