Game Theory

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By Silviu Guiasu, M. Malitza

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Vestal. Interacting Particle Systems for the Computation of Rare Credit Portfolio Losses. Finance and Stochastics, vol. 13, no. 4, 2009 pp. 613–633 (2009). 12. J. F. Carri`ere. Valuation of the Early-Exercise Price for Options using Simulations and Nonparametric Regression. Insurance : Mathematics and Economics, 19, 19–30 (1996). 13. R. Casarin. Simulation Methods for Nonlinear and Non-Gaussian Models in Finance. Premio SIE, Rivista Italiana degli Economisti, vol. 2, pp. 341–345 (2005). 14. R. Casarin and C.

In the same vein, and whenever possible, it can also be used as a technical tool to reduce the analysis of Snell approximation models on compact state spaces or even on finite but possibly large quantization trees or Monte Carlo grids. This perturbation analysis is clearly not new, it has been used with success in [25, 29, 44, 65] in the context of nonlinear filtering semigroups and particle approximation models. In the context of optimal stopping problems and numerical quantization schemes, these techniques were also used for instance in the papers of Egloff [38] and Gobet et al.

X1 … U1 ; : : : ; XT … UT / that the trajectory does enter at least one of these subsets. The key idea is to introduce a series of intermediate events interpolating between the series of the full state space E1 ; : : : ; ET of the path space and the target rare event series U1 ; : : : ; UT . 0/ D Fp : Then the state fcg appearing in (35) is defined in the construction of a new Markov chain in constant state space F WD F0 [ [ FT [ fcg. T C 1/ ^ inffp; Xp 2 Upj g with the convention that XT C1 WD c.

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