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- W4300786941 abstract "This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the classical Black-Scholes theory for pricing financial instruments, as well as models of stochastic dynamic portfolio optimization leading to the Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both problems can be represented by solutions to nonlinear parabolic equations. Qualitative analysis will be focused on issues concerning the existence and uniqueness of solutions. In the numerical part we discuss a stable finite-volume and finite difference schemes for solving fully nonlinear parabolic equations." @default.
- W4300786941 created "2022-10-04" @default.
- W4300786941 creator A5041720901 @default.
- W4300786941 date "2017-07-03" @default.
- W4300786941 modified "2023-10-16" @default.
- W4300786941 title "Nonlinear Parabolic Equations arising in Mathematical Finance" @default.
- W4300786941 doi "https://doi.org/10.48550/arxiv.1707.01436" @default.
- W4300786941 hasPublicationYear "2017" @default.
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