We overcome a major obstacle in mathematical optimization. In so doing, we provide a smooth solution to the HJB PDE without assuming the smoothness of the value function. We apply our method to financial models

We generalize and extend the previous results of the theory of the competitive firm under uncertainty. In doing so, we consider simultaneous output, output price and input price uncertainties. Our results do not impose the typical restrictions on the firm's preferences or utility. The...

We show that the distribution of the arithmetic, continuous average of log-normal variables is log-normal. We also introduce a simple, explicit formula for pricing the arithmetic Asian options. The pricing formula is as simple as the classical Black-Scholes formula

We devise a method to circumvent the complexity that arises from the option multi-dimensionality. That is, we transform the model to make it as simple as the one-dimensional case. Furthermore, the assumption of comonotonicity and other assumptions regarding the structure of the underlying asset...

We introduce a simple, exact and explicit formula for pricing the arithmetic Asian options. The pricing formula is as simple as the classical Black-Scholes formula. Our method is applicable to both the discrete and continuous averages

We provide explicit, simple price formulas for European options under stochastic volatility. The formulas are as simple as the classical Black-Scholes formula. We also explicitly include the volatility of volatility in the price formula