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Nonlinear PDEs risen when solving some optimization problems in finance, and their solutions

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  • Andrey Itkin

Abstract

We consider a specific type of nonlinear partial differential equations (PDE) that appear in mathematical finance as the result of solving some optimization problems. We review some existing in the literature examples of such problems, and discuss the properties of these PDEs. We also demonstrate how to solve them numerically in a general case, and analytically in some particular case.

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  • Andrey Itkin, 2015. "Nonlinear PDEs risen when solving some optimization problems in finance, and their solutions," Papers 1510.04899, arXiv.org.
    • Handle: RePEc:arx:papers:1510.04899
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    1. Li, Bo & Lu, Benzhuo & Wang, Zhongming & McCammon, J. Andrew, 2010. "Solutions to a reduced Poisson–Nernst–Planck system and determination of reaction rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1329-1345.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
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