A posited fuzzy-evolutionary computational model to minimise the tracking error of an option-replicating portfolio
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Received (in revised form): 21st May, 2007
Mohammad Khoshnevisan received his PhD degree specialising in computational finance from the University of Melbourne, Australia. In his doctoral thesis he developed an optimal control model for borrowing in the Australian petroleum industry. He has published a vast number of articles in international journals, conference proceedings and refereed monographs and many of his works are cited by elite academic/research organisations such as the American Mathematical Society and the International Statistical Institute. He is a senior lecturer in Finance at Griffith University, Australia. Edgars Vimba is presently a undergraduate student in the Department of Economics, Judd A. and Marjorie Weinberg College of Arts and Sciences at Northwestern University. He is double majoring in Economics and Mathematics. Edgars has been a member of the Sigma Beta Delta International Honor Society in Business, Management and Administration since 2006 and has won the prestigious President’s Foreign Student Scholarship (2004–2007) at Alaska Pacific University, USA. Sukanto Bhattacharya received his PhD degree in Information Technology from Bond University, Australia in 2004. He is an internationally recognised authority on fuzzy and neutrosophic optimal control models and their applications in financial risk management. He has many publications in international journals, conference proceedings, refereed monographs as well as a book chapter. His publications encompass a varied range of disciplines ranging from forensic accounting to quantum metaphysics. He is an assistant professor of Finance in the Department of International Business and Management at Dickinson College, USA.
Practical applications This article builds on an earlier work that used a Genetic Algorithm approach to computationally demonstrate the evolutionary optimality of the Black–Scholes function. We have extended the same computational scheme to posit a practically usable portfolio optimisation tool that could effectively minimise the cumulative hedging error of a replicating portfolio for a multi-asset, best-of option. Abstract In this paper, we build on an earlier work using a haploid genetic algorithm ( hGA) model that demonstrated the evolutionary optimality of the Black–Scholes options pricing functional form. We adopt the same hGA model in a similar problem context and posit adding on a fuzzy logic controller to come up with a practically usable
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portfolio management decision support tool that could minimise the cumulative hedging error. As the optimality constraints are dependent on abruptly changing and often ambiguous market conditions, it provides a fertile ground for applying such fuzzy optimisation. Journal of Derivatives & Hedge Funds (2007) 13, 214–219. doi:10.1057/palgrave.jdhf.1850075
Journal of Derivatives & Hedge Funds Volume 13 Number 3 2007 www.palgrave-journals.com/jdhf
Journal of Derivatives & Hedge Funds, Vol. 13 No. 3, 2007, pp. 214–219 r 2007 Palgrave Macmillan Ltd 1753-9641 $30.00
Keywords: hap
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