Emeritus Professor Eckhard Platen was holding the Chair in Quantitative Finance at the University of Technology Sydney. He published three books on numerical methods for stochastic differential equations, which are used as models in many areas of application, including finance, insurance, economics, telecommunication, biotechnology, epidemiology, marketing, voting behaviour, medicine, chemical reactions and electrical engineering. His fourth and fifths books are on his innovative benchmark approach, which generalize classical finance theory so that long-term risk management can be provided less expensively and more efficiently. He has advised leading banks and insurance companies worldwide. His main interests are focused on the extension and application of his benchmark approach towards a generalized approach to economics and finance.
In this paper the authors formulate the one-dimensional RMQ and d-dimensional PMQ algorithms as standard vector quantization problems by deriving the density, distribution and lower partial expectation functions of the random variables to be quantized at…