This paper studies a non-concave optimization problem under a Value-at-Risk (VaR) or an Expected Shortfall (ES) constraint. The non-concavity of the problem stems from the non-linear payoff structure of the optimizing investor. We obtain the closed-form optimal wealth with an ES constraint as...

We construct a dynamical credit model that can be calibrated exactly to CDS quotes. Modelling the default time as the first-passage time of a credit index process to the level zero, we show that the parameters of this credit index process can be chosen such that the risk-neutral (implied)...

Financial primitives are introduced to define acceptable loss exposures when demands and supplies are defined on differing event spaces. Acceptable loss exposures are modeled by a convex cone of random variables containing the non-negative random variables. The resulting financial equilibrium...

Risk management is developed by using implied volatilities associated with a Laplacian base density as opposed to the normal distribution. Expressions are derived for all the Laplacian greeks. The Laplacian implied volatilities and greeks are compared with their Gaussian counterparts....