Daily return distributions are modeled by pure jump limit laws that are selfdecomposable laws. The returns may be seen as composed of a sum of independent and identically distributed increments or as a selfsimilar law scaling the sum of exponentially weighted past shocks or a combination...

Prudent upper and lower valuations from the literature on arbitrage free two price economies provide risk characteristics driving required returns. The risk characteristics assess the risk of price fluctuations. The difference between the upper and lower prudent valuations can be viewed as a...

We propose a model of volatility tail behavior, in which investors display aversion to both low volatility and high volatility states, and, hence, the derived pricing kernel exhibits an increasing and decreasing region in the volatility dimension. The model features investors who have...