Труды сотрудников ИВМ СО РАН

[Text] : научное издание / S. Chang [et al.] // Computational Research. - 2014. - Vol. 2, Is. 3. - p. 49-53DOI 10.13189/cr.2014.020303 . -
Аннотация: In this paper, fitted finite volume method is developed to solve a nonlinear degenerate Black-Scholes equation applied in the valuation of unit-linked policy with surrender option, based on the fitting idea in S. Wang [IMA J. Numer. Anal., 24 (2004), 699-720]. Unlike the conventional pricing method mentioned in [1] which is using the free boundary method to calibrate the valuation PDE, here we develop a power penalty method to solve numerically the linear complimentary problem in the variational inequality arising from the valuation of unit-linked policy with surrender option. With the degenerate boundary and non-smooth final condition, we will show that it is essential to refine the mesh to remain the convergence and super-convergence order.

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Доп.точки доступа:
Chang, Shuhua; Добронец, Борис Станиславович; Fang, Zhiwei; Liu, Xin; Shaydurov, V.V.; Шайдуров, Владимир Викторович

/ V. V. Shaidurov, V. S. Kornienko // J. Siberian Fed. Univ. Humanit. Social Sci. - 2019. - Vol. 12, Is. 4. - P701-715, DOI 10.17516/1997–1370–0418. . - ISSN 1997-1370
Аннотация: The article is a review of modern mathematical economic models with the “Mean Field Games” structure. They are currently used for the predictive modelling under given control conditions or for optimizing control actions to achieve the desired result. The mathematical model is a pair of parabolic partial differential equations with a set of initial and boundary conditions for optimizing a given target functional. For them, the discretization is applied to obtain systems of nonlinear algebraic equations which are solved by computer in an iterative way to get the best instant benefit for each agent. This mathematical apparatus is used for the quantitative modelling of the distribution or the use of alternative resources, environmental problems, optimization of wages and insurance, network sales, and other economic activities to predict the aggregate behavior of the great mass of agents looking for instant personal benefit. © Siberian Federal University. All rights reserved.

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Держатели документа:
Institute of Computational Modeling SB RAS, 50/44 Akademgorodok, Krasnoyarsk, 660036, Russian Federation
Tianjin University of Finance and Economics, 25 Zhujiang Road, Hexi District, Tianjin, 300222, China
Siberian Federal University, 79 Svobodny, Krasnoyarsk, 660041, Russian Federation

Доп.точки доступа:
Shaidurov, V. V.; Kornienko, V. S.

/ V. V. Shaidurov, V. S. Kornienko // J. Siberian Fed. Univ. Humanit. Social Sci. - 2019. - Vol. 12, Is. 4. - P701-715, DOI 10.17516/1997–1370–0418 . - ISSN 1997-1370
Аннотация: The article is a review of modern mathematical economic models with the "Mean Field Games" structure. They are currently used for the predictive modelling under given control conditions or for optimizing control actions to achieve the desired result. The mathematical model is a pair of parabolic partial differential equations with a set of initial and boundary conditions for optimizing a given target functional. For them, the discretization is applied to obtain systems of nonlinear algebraic equations which are solved by computer in an iterative way to get the best instant benefit for each agent. This mathematical apparatus is used for the quantitative modelling of the distribution or the use of alternative resources, environmental problems, optimization of wages and insurance, network sales, and other economic activities to predict the aggregate behavior of the great mass of agents looking for instant personal benefit. © Siberian Federal University. All rights reserved.

Scopus,
Смотреть статью

Держатели документа:
Institute of Computational Modeling SB RAS, 50/44 Akademgorodok, Krasnoyarsk, 660036, Russian Federation
Tianjin University of Finance and Economics, 25 Zhujiang Road, Hexi District, Tianjin, 300222, China
Siberian Federal University, 79 Svobodny, Krasnoyarsk, 660041, Russian Federation

Доп.точки доступа:
Shaidurov, V. V.; Kornienko, V. S.