CLOSED FORM INTEGRATION OF ARTIFICIAL NEURAL NETWORKS WITH SOME APPLICATIONS TO FINANCE

Many economic and econometric applications require the integration of functions lacking a closed form antiderivative, which is therefore a task that can only be solved by numerical methods. We propose a new family of probability densities that can be used as substitutes and have the property of closed form integrability. This is especially advantageous in cases where either the complexity of a problem makes numerical function evaluations very costly, or fast information extraction is required for nonparametric maximum likelihood density estimation and may thus find a variety of applications, two of which are illustrated briefly:- Estimation of 'Value at Risk' based on approximations to the density of stock returns.- Recovering risk neutral densities for the valuation of options from the option price - strike price relation.