Optimization in financial engineering - an essay on 'good' solutions and misplaced exactitude

We discuss the precision with which financial models are handled, in particular optimization models. We argue that precision is only required to a level that is justified by the overall accuracy of the model, and that this required precision should be specifically analyzed in order to better appreciate the usefulness and limitations of a model. In financial optimization, such analyses are often neglected; operators and researchers rather show an a priori preference for numerically-precise methods. We argue that given the (low) empirical accuracy of many financial models, such exact solutions are not needed; 'good' solutions suffice. Our discussion may appear trivial: everyone knows that financial markets are noisy, and that models are not perfect. Yet the question of the appropriate precision of models with regard to their empirical application is rarely discussed explicitly; specifically, it is rarely discussed in university courses on financial economics and financial engineering. Some may argue that the models’ errors are understood implicitly, or that in any case more precision does no harm. Yet there are costs. We seem to have a built-in incapacity to intuitively appreciate randomness and chance. All too easily then, precision is confused with actual accuracy, with potentially painful consequences.