Geodesic
The combined Monte-Carlo method to calculate the capital of the optimal portfolio in nonlinear models of financial indexes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 1021-1034

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The calculations in models of random processes with influence of events are considered. The trajectories of these processes are continuous concatenation of trajectories of diffusion processes with constant coefficients. The suggested method is the combination of the Monte-Carlo method and exact calculation. The examples of popular models, for which investigated models can be used as the approximation, are presented.
Keywords: Monte-Carlo method, Black–Scholes formula, stochastic volatility. 
@article{SEMR_2014_11_a39,
     author = {G. I. Beliavsky and N. V. Danilova},
     title = {The combined {Monte-Carlo} method to calculate the capital of the optimal portfolio in nonlinear models of financial indexes},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1021--1034},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a39/}
}
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G. I. Beliavsky; N. V. Danilova. The combined Monte-Carlo method to calculate the capital of the optimal portfolio in nonlinear models of financial indexes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 1021-1034. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a39/