1,721,001 research outputs found
An Alternative Method for Calculating the Probability of Ruin in Risk Theory. Theoretical Approach and Applications
No full textAbout the Calculation of the Total Claims Distribution: An Alternative Procedure Aimed to Avoid the Undeflow and Overflow Problems of the Traditional Recursive Formula
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Le funzioni con memoria come strumento di valutazione delle opzioni americane
No full textDottorato di ricerca in matematica per l'analisi dei mercati finanziari. 7. cicloConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal
Pricing arithmetic average options and basket options using Monte Carlo and Quasi-Monte Carlo methods
Get PDFIn the present paper, we address the evaluation problem of multidimensional financial options. We apply in particular the Monte Carlo and Sobol Quasi-Monte Carlo numerical integration for pricing asian arithmetic average options and basket options and we show some numerical exemplifications in 4 and 12 dimensions. The paper is the occasion to furtherly test the algorithm for computing the quantile function of the standard gaussian distribution proposed by the authors in a previous publication
On the Calculation of Convolution in Actuarial Applications. A Case Study using Discrete Random Variables
No full textIn literature, the sum of discrete random variables becomes a problem of heavy (and often impracticable) computation no sooner does the number of convolutions exceed few units. In this paper, we show how this problem can be easily overcome in actuarial applications when using random variables with integer (positive, negative, or null) or referable to integer numerical realizations but not necessarily identically distributed. Under the above-mentioned condition, we illustrate in particular two exact methods and an approximated one for calculating convolution: - the first exact method is based on the well-known Fast Fourier Transform (FFT); - the second exact method is derived from the classical approach using Discrete Fourier Transform (DFT) by means of algebraic manipulations; - the third method is derived from the definition of convolution and it is approximated by neglecting the probabilities less than a given bound ? =10-h (51?h?100)**. As for the error bounds of the approximated method, it is worth noting that the results obtained by this method differ in relative terms from the corresponding exact values of less than 10-9. This can be tested by comparing the convoluted probability distribution obtained by the approximated method with the one obtained by the other two methods and by also comparing the first four moments with those computed directly on the original random variables. The results (in particular the exact and the approximated probability distribution) are identical in practice. It does not exist therefore the problem of a difference along the tail. As a consequence, although the proposed method is an “approximated method” under a mathematical point of view, it can be considered an “exact method” in the actuarial applications. As for the efficiency of calculation, we show that, generally speaking, the approximated method performs better (also thanks to the substantial simplification obtained by summing, after each convolution, the probabilities corresponding to the same numerical realizations) than both the exact methods
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