A financial market of a stochastic delay equation
Bull. Korean Math. Soc. 2019 Vol. 56, No. 5, 1129-1141
https://doi.org/10.4134/BKMS.b180848
Published online September 30, 2019
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
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