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Czichowsky, C., Peyre, R., Schachermayer, W. and Yang, J. (2018) Shadow Prices, Fractional Brownian Motion, and Portfolio Optimisation under Transaction Costs. Finance and Stochastics, 22, 161-180. https://doi.org/10.1007/s00780-017-0351-5

has been cited by the following article:

• TITLE: Perpetual American Call Option under Fractional Brownian Motion Model

  AUTHORS: Atsuo Suzuki

  KEYWORDS: Option Pricing, Fractional Brownian Motion, Optimal Stopping Boundary

  JOURNAL NAME: Journal of Mathematical Finance, Vol.13 No.2, May 31, 2023

  ABSTRACT: In this paper, we consider perpetual American options under a fractional Brownian motion and give the closed-form solution for their value function. We discuss the pricing model when the underlying asset pays dividends continuously and derive the value functions. In order to get an analytical solution, we use the quadratic approximation method. By this approximation, we have Black-Scholes ordinary differential equation. Solving this equation with the boundary conditions, we get the value function and its optimal boundary.