Fadugba, S.E.2019-01-222019-01-222017-05ui_thesis_fadugba_mellin_2017http://ir.library.ui.edu.ng/handle/123456789/4056A Thesis in the Department of Mathematics, Submitted to the Faculty of Science in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY of the UNIVERSITY OF IBADANAn p (Sn t ; t) = 1 2 i Z c+i1 c􀀀i1 K!+1 !(! + 1) e 1 2n2 2(!2+ 1!􀀀 2)(T􀀀t)(Sn t )􀀀!d! + rK 2 i Z c+i1 c􀀀i1 Z T t (Sn t )􀀀! ( Sn y )! ! e 1 2n2 2(!2+ 1 !􀀀 2)(y􀀀t)dyd! 􀀀 q 2 i Z c+i1 c􀀀i1 Z T t (Sn t )􀀀! ( Sn y )!+1 ! + 1 e 1 2n2 2(!2+ 1 !􀀀 2)(y􀀀t)dyd!enAmerican power put option,Geometric Brownian motionIto's lemmaNon-homogeneous Black-Scholes-Merton-like equationValue-matching conditionThesis