Stochastic optimal investment in a stable paretian stock market

Abstract

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.