hal-00607105
https://paris1.hal.science/hal-00607105
[SHS] Sciences de l'Homme et de la Société
[UNIV-PARIS1] Université Panthéon-Sorbonne - Paris I
[CNRS] CNRS - Centre national de la recherche scientifique
[UNIV-CERGY] Université de Cergy Pontoise
[CES] Centre d'Economie de la Sorbonne
[AO-ECONOMIE] Archives ouvertes de l'Economie
[THEMA-UMR8184] Théorie économique, modélisation et applications
[CY-TECH-SM] CY TECH : Sciences de la modélisation
PORTFOLIO OPTIMIZATION WITHIN MIXTURE OF DISTRIBUTIONS
Hentati, Rania
Prigent, Jean-Luc
JEL : C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C61 - Optimization Techniques • Programming Models • Dynamic Analysis
JEL : G - Financial Economics/G.G1 - General Financial Markets/G.G1.G11 - Portfolio Choice • Investment Decisions
[QFIN.PM] Quantitative Finance [q-fin]/Portfolio Management [q-fin.PM]
COMM
Portfolio optimization
Mixture probability distributions
The recent financial crisis has highlighted the necessity to introduce mixtures of probability distributions in order to improve the estimation of asset returns and in particular to better take account of risks. Since Pearson (1894), these mixtures have been intensively used in many scientific fields since they provide very convenient mathematical tools to examine various statistical data and to approximate many probability distributions. They are typically introduced to model the choice of probability distributions among a given parametric family. The coefficients of the mixture usually correspond to the relative frequencies of each possible parameter. In this framework, we examine the single-period portfolio choice model, which has been addressed in the partial equilibrium framework, by Brennan and Solanki (1981), Leland (1980) and Prigent (2006). We consider an investor who wants to maximize the expected utility of the value of his portfolio consisting of one risk-free asset and one risky asset. We provide and analyze the solution for log return with mixture distributions, in particular for the mixture Gaussian case. The optimal portfolio is characterized for arbitrary utility functions. Our results show that mixture of distributions can have significant implications on the portfolio management.
2011-06-29
en
National and Kapodistrian University of Athens, Greece
International Conference on Applied Financial Economics
samos, Greece