Computational theories and techniques in finance

Futures and options have unleashed the value of future states into our present. They have augmented the supply and the liquidity of money, the availability of credit and have contributed immensely to financial exchanges and the development of financial markets. We owe therefore great thanks to the extraordinary contributions of economists such as Kenneth Arrow, Gerard Debreu, Lucas, Fisher Black, Myron Scholes and Robert Merton. The underlying state preference theories and their engineered pricing models have raised numerous challenges to computational theories and techniques seeking to bridge economic science with its practical use – even though its application might be less than perfect. While financial modeling requires structured stochastic models with specific mathematical properties, theoretically justifiable within the Arrow–Debreu state preference theory, its application to real problems can only be assessed ex-post – whether it works or it does not. We are all aware that many underlying assumptions of financial models may be wrong and at times leading to contradictions to finance’s fundamental theory. For example, questions arise regarding: