Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2019; 56(5): 1129-1141

Online first article July 23, 2019      Printed September 30, 2019

https://doi.org/10.4134/BKMS.b180848

Copyright © The Korean Mathematical Society.

A financial market of a stochastic delay equation

Ki-Ahm Lee, Kiseop Lee, Sang-Hyeon Park

Seoul National University; Purdue University; Daishin Securities

Abstract

We propose a stochastic delay financial model which describes influences driven by historical events. The underlying is modeled by stochastic delay differential equation (SDDE), and the delay effect is modeled by a stopping time in coefficient functions. While this model makes good economical sense, it is difficult to mathematically deal with this. Therefore, we circumvent this model with similar delay effects but mathematically more tractable, which is by the backward time integration. We derive the option pricing equation and provide the option price and the perfect hedging portfolio.

Keywords: stochastic delay model, hedging, option

MSC numbers: Primary 91G20, 60G99