"A New Improvement Scheme for Approximation Methods of Probability Density Functions"
   This paper develops a new scheme for improving an approximation method of a probability density function, which is inspired by the idea in<em> the Hilbert space projection theorem</em>. Moreover, we apply “Dykstra's cyclic projections algorithm†for its implementation. Numerical examples for application to an symptotic expansion method in option pricing demonstrate the effectiveness of our scheme under SABR model.