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# On the convergence of the quasi-regression method: polynomial chaos and regularity

## Abstract

We present an analysis of convergence of a quasi-regression Monte Carlo method proposed by Glasserman and Yu (2004). We show that the method surely converges to the true price of an American option even under multiple underlyings via polynomial chaos expansion and weaker conditions than those used in Glasserman and Yu (2004). Further, we show the number of simulation paths grows exponentially in the number of basis functions to obtain convergence in implementing the method. Finally, we propose a rate of convergence considering regularity of value functions.

## Corresponding author

* Postal address: SKK Business School, SungKyunKwan University, 25-2, Sungkyunkwan-ro, Jongno-gu, Seoul 03063, Republic of Korea. Email address: jkim74@vols.utk.edu

## References

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# On the convergence of the quasi-regression method: polynomial chaos and regularity

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