This work has been wholly adapted from the dissertation submitted by the author in 2004 to the Faculty of Information Technology, Bond University, Australia in fulfillment of the requirements for his doctoral qualification in Computational Finance. This work covers a substantial mosaic of related concepts in utility theory as applied to financial decision-making. The main body of the work is divided into four relevant chapters. The first chapter takes up the notion of resolvable risk i.e. systematic investment risk which may be attributed to actual market movements as against irresolvable risk which is primarily born out of the inherent imprecision associated with the information gleaned out of market data such as price, volume, open interest etc. A neutrosophic model of risk classification is proposed – neutrosophic logic being a new branch of mathematical logic which allows for a three-way generalization of binary fuzzy logic by considering a third, neutral state in between the high and low states associated with binary logic circuits. A plausible application of the postulated model is proposed in reconciliation of price discrepancies in the long-term options market where the only source of resolvable risk is the long-term implied volatility. The chapter postulates that inherent imprecision in the way market information is subjectively processed by psycho-cognitive factors governing human decision-making actually contributes to the creation of heightened risk appraisals. Such heightened notions of perceived risk make investors predisposed in favor of safe investments even when pure economic reasoning may not entirely warrant such a choice. To deal with this information fusion problem a new combination rule has been proposed - the Dezert-Smarandache combination rules of paradoxist sources of evidence, which looks for the basic probability assignment or bpa denoted as m (.) = m1(.)(+)m2(.) that maximizes the joint entropy of the two information sources.

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