24 research outputs found
Adomian decomposition method for analytical solution of a continuous arithmetic Asian option pricing model
One of the main issues of concern in financial mathematics has been a viable method for
obtaining analytical solutions of the Black-Scholes model associated with Arithmetic Asian Option (AAO).
In this paper, a proposed semi-analytical technique: Adomian Decomposition Method (ADM) is applied for
the first time, for analytical solution of a continuous arithmetic Asian option model. The ADM gives the
solution in explicit form with few iterations. The computational work involved is less. However, high level of
accuracy is not neglected. The obtained solution conforms with those of Rogers and Shi (J. of Applied
Probability 32: 1995, 1077-1088), and Elshegmani and Ahmad (ScienceAsia, 39S: 2013, 67–69). Thus, the
proposed method is highly recommended for analytical solution of other versions of Asian option pricing
models such as the geometric form for puts and calls, even in their time-fractional forms
ITERATIVE METHOD FOR CONSTRUCTING ANALYTICAL SOLUTIONS TO THE HARRY-DYM INITIAL VALUE PROBLEM
In this paper, an analytical technique, namely the new iterative method (NIM), is applied to obtain an approximate analytical solution of the nonlinear Harry-Dym equation which is often used in the theory of solitons. The rapid convergence of the method results in qualitatively accurate solutions in relatively few iterations; this is obvious upon comparing the obtained analytical solutions with the exact solutions. Our results indicate that NIM is highly accurate and efficient, therefore can be considered a very useful and valuable method