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Multivariate Affine GARCH in portfolio optimization. Analytical solutions and applications

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  • Escobar-Anel, Marcos
  • Yang, Yu-Jung
  • Zagst, Rudi

Abstract

This paper develops an optimal portfolio allocation formula for multi-assets where the covariance structure follows a multivariate Affine GARCH(1,1) process. We work under an expected utility framework, considering an investor with constant relative risk aversion (CRRA) utility who wants to maximize the expected utility from terminal wealth. After approximating the self-financing condition, we derive closed-form expressions for all the quantities of interest to investors: optimal allocations, optimal wealth process, and value function. Such a complete analytical solution is a first in the GARCH multivariate literature. Our empirical analyses show a significant impact of multidimensional heteroscedasticity in portfolio decisions compared to a setting of constant covariance as per Merton’s embedded solution.

Suggested Citation

  • Escobar-Anel, Marcos & Yang, Yu-Jung & Zagst, Rudi, 2025. "Multivariate Affine GARCH in portfolio optimization. Analytical solutions and applications," The North American Journal of Economics and Finance, Elsevier, vol. 77(C).
    • Handle: RePEc:eee:ecofin:v:77:y:2025:i:c:s1062940825000166
    DOI: 10.1016/j.najef.2025.102376
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    Cited by:

    1. Ayush Jha & Abootaleb Shirvani & Ali Jaffri & Svetlozar T. Rachev & Frank J. Fabozzi, 2025. "Multivariate Affine GARCH with Heavy Tails: A Unified Framework for Portfolio Optimization and Option Valuation," Papers 2505.12198, arXiv.org.

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    More about this item

    Keywords

    Expected utility; CRRA utility; Multivariate affine GARCH; Portfolio optimization;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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