Studied is the distribution of stock returns in the Korean stock exchange market. We present some empirical evidence which indicates that the distribution of stock returns can be represented by a member of the stable Paretian family of distributions. The parameters of the stable Paretian distribution are estimated by a moment matching method, and goodness of fit tests are conducted by kurtosis and chi-square. Stability and stationarity are also tested. We develope portfolio analysis models based on a safety first and stochastic dominance rules when the stock returns are distributed with a univariate symmetric jointly independent, or a multivariate symmetric jointly interdependent, stable Paretian distribution having a characteristic exponent less than two. This paper also developes optimal investment models in the safety first and stochastic dominance rules with risk free assets.