This chapter deals with nonparametric estimation of the risk neutral density. We present three different approaches … of the risk neutral density. The first estimator is a kernel smoother of the second derivative of call prices, while the … we assume the existence of a stochastic discount factor (pricing kernel) which establishes the risk neutral density …

We propose a new approach to optimal portfolio selection in a downside risk framework that allocates assets by … maximizing expected return subject to a shortfall probability constraint, reflecting the typical desire of a risk-averse investor …-used mean-variance approach based on the cumulative cash values, geometric mean returns, and average risk-adjusted returns. We …