Abstract
This paper studies the nonlinear variational inequality with integro-differential term arising from valuation of American style double barrier option. First, the authors use the penalty method to transform the variational inequality into a nonlinear parabolic initial boundary problem (i.e., penalty problem). Second, the existence and uniqueness of solution to the penalty problem are proved by using the Scheafer fixed point theory. Third, the authors prove the existence of variational inequality’ solution by showing the fact that the penalized PDE converges to the variational inequality. The uniqueness of solution to the variational inequality is also proved by contradiction.
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This research is supported by the National Science Foundation of China under Grant Nos. 71171164 and 70471057, the Doctorate Foundation of Northwestern Polytechnical University under Grant No. CX201235.
This paper was recommended for publication by Editor WANG Shouyang.
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Sun, Y., Shi, Y. & Gu, X. An integro-differential parabolic variational inequality arising from the valuation of double barrier American option. J Syst Sci Complex 27, 276–288 (2014). https://doi.org/10.1007/s11424-014-2218-6
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DOI: https://doi.org/10.1007/s11424-014-2218-6