The distribution function of a weighted sum of weakly correlated non-identical lognormal random variables is required in various fields of science and engineering and specifically in finance for portfolio management as well as exotic options valuation. Unfortunately, it has no known closed form...

This paper points out to loopholes in Modern Portfolio Theory (MPT) and fundamental flaws that question its validity and applicability not only for investment but for education as well. Using theoretical analysis, Monte Carlo simulations and market data I present and discuss theoretical, as well...

The basic Lucas model for risky R&D projects is revisited. New solutions for optimal expenditures are explored by exploiting the merits of the theory of differential equations. After applying the calculus of variations, a nonlinear differential equation is presented whose solution provides the...