2019/03/10 by O Hyong-Chol, O, Hyong-chol, Song-San Jo +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #35A35 #39A12 #62P05 #91B28 #Climate Change Policy and Economics #Economic theories and models #FOS: Economics and business #Innovation Diffusion and Forecasting #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1903.05189
openalex publication_date 2019/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A variational inequality for pricing the perpetual American option and the\ncorresponding difference equation are considered. First, the maximum principle\nand uniqueness of the solution to variational inequality for pricing the\nperpetual American option are proved. Then the maximum principle, the existence\nand uniqueness of the solution to the difference equation corresponding to the\nvariational inequality for pricing the perpetual American option and the\nsolution representation are provided and the fact that the solution to the\ndifference equation converges to the viscosity solution to the variational\ninequality is proved. It is shown that the limits of the prices of variational\ninequality and BTM models for American Option when the maturity goes to\ninfinity do not depend on time and they become the prices of the perpetual\nAmerican option.\n