## The Problem Of Optimal Asset Allocation With Stable Distributed Returns (2004)

Venue: | Stochastic Processes and Functional Analysis, Dekker Series of Lecture Notes in Pure and Applied Mathematics |

Citations: | 7 - 4 self |

### BibTeX

@INPROCEEDINGS{Ortobelli04theproblem,

author = {Sergio Ortobelli and Eduardo Schwartz},

title = {The Problem Of Optimal Asset Allocation With Stable Distributed Returns},

booktitle = {Stochastic Processes and Functional Analysis, Dekker Series of Lecture Notes in Pure and Applied Mathematics},

year = {2004},

pages = {295--361}

}

### OpenURL

### Abstract

This paper discusses two optimal allocation problems. We consider different hypotheses of portfolio selection with stable distributed returns for each of them. In particular, we study the optimal allocation between a riskless return and risky stable distributed returns. Furthermore, we examine and compare the optimal allocation obtained with the Gaussian and the stable non-Gaussian distributional assumption for the risky return. KEY WORDS: optimal allocation, stochastic dominance, risk aversion, measure of risk, a stable distribution, domain of attraction, sub-Gaussian stable distributed, fund separation, normal distribution, mean variance analysis, safety-first analysis. 2 1. INTRODUCTION This paper serves a twofold objective: to compare the normal with the stable non-Gaussian distributional assumption when the optimal portfolio is to be chosen and to propose stable models for the optimal portfolio selection according to the utility theory under uncertainty. It is well-known that asset returns are not normally distributed, but many of the concepts in theoretical and empirical finance developed over the past decades rest upon the assumption that asset returns follow a normal distribution. The fundamental work of Mandelbrot (1963a-b, 1967a-b) and Fama (1963,1965a-b) has sparked considerable interest in studying the empirical distribution of financial assets. The excess kurtosis found in Mandelbrot's and Fama's investigations led them to reject the normal assumption and to propose the stable Paretian distribution as a statistical model for asset returns. The Fama and Mandelbrot's conjecture was supported by numerous empirical investigations in the subsequent years, (see Mittnik, Rachev and Paolella (1997) and Rachev and Mittnik (2000)). The practical and theoretical app...