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Optimal Consumption and Portfolio in a Jump Diffusion Market with Proportional Transaction Costs

Nils Chr. Framstad Bernt Oksendal Agnès Sulem 1
1 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
Abstract : We study the optimal consumption and portfolio in a jump diffusion market with proportional transaction costs. We show that the solution in the jump diffusion case has the same form as in the pure diffusion case; in particular, (under some assumptions) there is a transaction cone D such that it is optimal to make no transactions as long as the wealth position remains in D and to sell/buy stocks according to local time on the boundary of D. The associated integro-differential variational inequality is studied by using the theory of viscosity solutions.
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https://hal.inria.fr/inria-00072913
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Submitted on : Wednesday, May 24, 2006 - 11:16:00 AM
Last modification on : Friday, February 4, 2022 - 3:10:15 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:27:35 PM

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Nils Chr. Framstad, Bernt Oksendal, Agnès Sulem. Optimal Consumption and Portfolio in a Jump Diffusion Market with Proportional Transaction Costs. [Research Report] RR-3749, INRIA. 1999. ⟨inria-00072913⟩

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