(1+2)-dimensional Black-Scholes equations with mixed boundary conditions

Junkee Jeon; Jehan Oh

doi:10.3934/cpaa.2020032

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2020, Volume 19, Issue 2: 699-714. Doi: 10.3934/cpaa.2020032

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(1+2)-dimensional Black-Scholes equations with mixed boundary conditions

Junkee Jeon^1, and
Jehan Oh^2, ,

1.
Department of Applied Mathematics & Institute of Natural Science, Kyung Hee University, Yongin, 17104, Republic of Korea
2.
Department of Mathematics, Kyungpook National University, Daegu, 41566, Republic of Korea

^* Corresponding author
^* Corresponding author

Received: September 2018

Revised: April 2019

Published online: February 2020

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Abstract

In this paper, we investigate (1+2)-dimensional Black-Scholes partial differential equations(PDE) with mixed boundary conditions. The main idea of our method is to transform the given PDE into the relatively simple ordinary differential equations(ODE) using double Mellin transforms. By using inverse double Mellin transforms, we derive the analytic representation of the solutions for the (1+2)-dimensional Black-Scholes equation with a mixed boundary condition. Moreover, we apply our method to European maximum-quanto lookback options and derive the pricing formula of this options.

Keywords:

(1+2)-dimensional Black-Scholes equations,
parabolic partial differential equations,
double-Mellin transform,
mixed boundary condition,
option pricing.

Mathematics Subject Classification: 35K20.

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References

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