In the continuous case, this is obtained by. Several sets of numerical results are included. Statistical Mechanics and its Applications
Our technique is based on the Hermite polynomial expansion that can match exactly the first m moments of the model implied-probability distribution. We consider the problem where a manager aims to minimize the probability of his portfolio return falling below asian baskt option threshold while keeping the expected return no worse than a target, under the assumption that stock returns are Log-Normally distributed. We also extend our results to the design of basket options. The resulting integration problem is calculated by a suited quasi Monte Carlo method.
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