Beyond Simple Monte-Carlo: Parallel Computing with QuantLib
Beyond Simple Monte-Carlo: Parallel Computing with QuantLib
Beyond Simple Monte-Carlo: Parallel Computing with QuantLib
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Quasi <strong>Monte</strong>-<strong>Carlo</strong> on GPUs: Overview◮ Koksma-Hlawka bound is the basis for any QMC method:1∣nn∑∫f (x i ) − f (u)du∣ ≤ V (f )D ∗ (x 1 , ..., x n )[0,1] di=1D ∗ (log n)d(x 1 , ..., x n ) ≥ cn◮ The real advantage of QMC shows up only after N ∼ e ddrawing samples, where d is the dimensionality of the problem.◮ Dimensional reduction of the problem is often the first step.◮ The Brownian bridge is tailor-made to reduce the number ofsignificant dimensions.Klaus Spanderen<strong>Beyond</strong> <strong>Simple</strong> <strong>Monte</strong>-<strong>Carlo</strong>: <strong>Parallel</strong> <strong>Computing</strong> <strong>with</strong> <strong>QuantLib</strong>
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