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We revise some mathematical morphological operators such as Dilation, Erosion, Opening and Closing. We show proofs of our theorems for the above operators when the structural elements are partitioned. Our results show that structural elements can be partitioned before carrying out morphological operations.

Evolutionary computation have been used in different areas of research in finance. The more the perfect price of option we obtain the more attractive it becomes to the investors. Investors have developed much interest in option investment but when the option is exercised at a wrong time, it can lead to massive loss for the investor. This paper is mainly focused on pricing a European put option when the underlying security price is geometric mean reverting with the assumption that the Girsanov change of measure has already been implemented and it has a constant interest rate. We provide a Genetic Algorithm which gives a J. Ackora-Prah, P. S. Andam, S. A Gyamera and D. Gyamfi perfect option price needed to be redeemed by the option buyer so as the option seller gets some profit rather than the asset expiring worthless.

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