A greedy kernel-based partition of unity method for multi-asset American option problems
کد مقاله : 1026-FEMATH-FULL (R1)
1یاسین فدایی *، 2محمود محسنی مقدم
1دانشگاه شهید باهنر
2استاد دانشگاه شهید باهنر
چکیده مقاله:
In this paper we use a greedy algorithm on a kernel-based partition of unity method for the solutionnof multi-asset American option problems. This method can be overcome on a number of challenges for the kernel-based methods such as dense matrices and ill-conditioning. In the greedy algorithmnwe take a large finite subset $X$ as data points, then for a fixed domain, a fixed kernel and a fixed scale, this algorithm gives the first $N$ Newton basis functions on $N$ points,nand provides a subset of best trial points among the data site $X$.n The optimal trial points for interpolation obtainednamong a huge set of initial points and are used for kernel-based partition of unity method.This paper shows that selection nodes greedily yields thenbetter conditioning and reduceing the computational cost for the option pricing problem. Also, we add a small and continuous penalty term to the Black-Scholes equation to remove the free and moving boundary.
کلیدواژه ها:
American option, Kernel-based method, Greedy algorithm, Partition of unity, Radial basis function.
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