  Entropy based ideas find wide-ranging applications in finance for calibrating
models of portfolio risk as well as options pricing. The abstracted problem,
extensively studied in the literature, corresponds to finding a probability
measure that minimizes relative entropy with respect to a specified measure
while satisfying constraints on moments of associated random variables. These
moments may correspond to views held by experts in the portfolio risk setting
and to market prices of liquid options for options pricing models. However, it
is reasonable that in the former settings, the experts may have views on tails
of risks of some securities. Similarly, in options pricing, significant
literature focuses on arriving at the implied risk neutral density of benchmark
instruments through observed market prices. With the intent of calibrating
models to these more general stipulations, we develop a unified entropy based
methodology to allow constraints on both moments as well as marginal
distributions of functions of underlying securities. This is applied to
Markowitz portfolio framework, where a view that a particular portfolio incurs
heavy tailed losses is shown to lead to fatter and more reasonable tails for
losses of component securities. We also use this methodology to price
non-traded options using market information such as observed option prices and
implied risk neutral densities of benchmark instruments.
