Laplace and Mellin go Green G. Alobaidi, R. Mallier and M. C. Haslam Received: July 7, 2013; Revised: February 2, 2014; Accepted: February 28, 2014 Abstract. We use Mellin and Laplace transforms to study the price of American options, and show that both transforms produce solutions and integral equations which are equivalent to the Green's function approach. Conventional rather than partial transforms are used. We also combine a boundary fixing transformation with the integral transforms. Keywords: American options; integral transform; Laplace transform; Mellin transform; free boundary. AMS Subject classification: Primary: 91B28 Version to read: PDF ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2014, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |