The risk conscious investor is defined as the maximizer of a conservative valuation or dynamically a nonlinear …

A time homogeneous, purely discontinuous, parsimonous Markov martingale model is proposed for the risk neutral dynamics … additionally reported. It is observed that risk neutral dynamics by and large reflect the presence of momentum in numerous … probabilities. However, there is some reversion in the upper quantiles of risk neutral return distributions …

Allowing for correlated squared returns across two consecutive periods, portfolio theory for two periods is developed …

Two price economy principles motivate measuring risk by the cost of acquiring the opposite of the centered or pure risk … position at its upper price. Asymmetry in returns leads to differences in risk charges for short and long positions. Short risk … appropriate risk charge is minimized to construct two frontiers, one for the positive, and the other for negative, mean return …

components. Asset values, bid and ask, are given by conservative valuation operators from the theory of two price economies. The …

economy. When risk acceptability is completely defined by the risk distribution function and bid prices are additive for … market risk attitudes. Procedures are outlined for observing the economic magnitudes for diversification benefits reflected … directionally sensitive risk measures that are in the same units as the rewards. A further contribution is the ability to construct …

Instantaneous risk is described by the arrival rate of jumps in log price relatives. Aggregate arrivals are infinite …. There is then no concept of a mean return compensating risk exposure. The only risk-free instantaneous return is zero. All … portfolios are subject to risk and there are only bad and better ways of holding risk. The univariate variance gamma model is …

reformulation of risk reward concepts in these terms. It is shown the exponential variation replaces the mean as a reward concept …. Risk is measured by the shaves and add-ons implicit in the bid and ask prices of two price economies. An analysis of … markets reveals that these two sided risk measures significantly impact rewards in the markets for stocks, stock spreads, and …