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- W164421609 abstract "Fully nonlinear partial dierential equations have been used in the literature when deriving models for optimal portfolio hedging under particular market dynamics. More precisely, some models lead to nding the solution of a Monge-Amp ere-type equation, together with the Black and Scholes model, when using a hyperbolic absolute risk aversion utility function in port- folio optimization. Following (13,14), we derive several simplied Monge-Amp ere equations for the determination for optimal portfolio strategies based on various market stochastics dynamics. This fully nonlinear equation does not necessarily admit an explicit solution so that numerical methods are required to obtain an approximate solution, and numerical techniques must be cho- sen appropriately. We extend previous works about a computational framework for the elliptic Monge-Amp ere equation into two directions: we relax the assumptions on the data to treat sta- tionary examples with singularities, and we address the non-stationary case by introducing an evolutive Monge-Amp ere equation. Preliminary numerical results are presented to validate the eciency and the robustness of the methods in the stationary case, and a novel computational method is proposed for the non-stationary one." @default.
- W164421609 created "2016-06-24" @default.
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- W164421609 date "2014-01-01" @default.
- W164421609 modified "2023-09-23" @default.
- W164421609 title "Computation of portfolio hedging strategies using a reduced Monge-Ampère equation" @default.
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