Abstract
The Hoggard–Whalley–Wilmott equation is introduced to model portfolios of European type options incorporating transaction costs. The model gives rise to a nonlinear parabolic partial differential equation (PDE), whose nonlinearity reflects the presence of transaction costs. We show analytically the existence of solutions which are not necessarily convex nor concave. Numerical treatments are also given, which are devised to effectively handle an infinite domain and unbounded solutions.
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Imai, H., Ishimura, N., Mottate, I. et al. On the Hoggard–Whalley–Wilmott Equation for the Pricing of Options with Transaction Costs. Asia-Pacific Finan Markets 13, 315–326 (2006). https://doi.org/10.1007/s10690-007-9047-8
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DOI: https://doi.org/10.1007/s10690-007-9047-8