A Financial Market of A Stochastic Delay Equation
Bull. Korean Math. Soc.
Published online July 23, 2019
ki-ahm Lee, ki-seop Lee, and Sang-Hyeon Park
Seoul National University, Purdue University, Daishin Securities
Abstract : We propose a stochastic delay financial model which describes influences driven by uncertain 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 provide the option price and the perfect hedging portfolio.
Keywords : Delay Model, Hedging, Option
MSC numbers : Primary 91G20, 60G99
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