This paper adapts the hybrid method, a combination of the Laplace transformation and the finite-difference approach, to the pricing of barrier-style options. The hybrid method eliminates the time steps and provides a highly accurate and precise numerical solution that can be rapidly obtained. This method is superior to lattice methods when trying to solve barrier-style options. Previous studies have tried to solve barrier-style options; however, there have continually been several disadvantages. Very small time steps and stock node spaces are needed to avoid undesirable numerically induced oscillations in the solution of barrier option. In addition, all the intermediate option prices must be computed at each time step, even though one may be only interested in the terminal price of barrier-style complex options. The hybrid method may also solve more complex problems concerning barrier-style options with various boundary constraints such as options with a time-varying rebate. In order to demonstrate the accuracy and efficiency of the proposed scheme, we compare our algorithm with several well-known pricing formulas of barrier-type options. The numerical results show that the hybrid method is robust, and provides a highly accurate solution and fast convergence, regardless of whether or not the initial asset prices are close to the barrier.Barrier option, Hybrid method, Laplace transform, Finite-difference method,

a b s t r a c tThis study aims to explore whether a regularly updated portfolio of outperforming hedge funds can consistently beat the corresponding hedge fund dataset index. If yes, moreover, the second question concerns whether portfolio optimization approaches can lead to an even better performance than the naïve equal-weighting method. The dataset spans the January-1994 to August-2008 period and is classified into four main categories -Macro, Equity Hedge, Relative Value and Event Driven. Based on a seven-factor model, this study applies the Step-SPA test to each category of funds and examines the statistical significance of the studentized fund alpha over the selection period of 3e7 years in length. A 'winner' portfolio of funds, namely, consisting of funds with statistically significant, positive studentized alpha, can be formed at the end of the selection period and held for 1 up to 3 years. We find that the winner portfolio tends to beat the dataset indexes during the holding period, irrespective of the time span for the selection and the holding periods investigated. Moreover, two of the three optimization approaches employed, the Probabilistic Global Search Lausanne and the Genetic Algorithm, prove to further enhance the performance of the equal-weighted winning portfolio.