Print Email Facebook Twitter Bayesian inference of the multi-period optimal portfolio for an exponential utility Title Bayesian inference of the multi-period optimal portfolio for an exponential utility Author Bauder, David (Humboldt-Universitat zu Berlin) Bodnar, Taras (Stockholm University) Parolya, N. (TU Delft Statistics) Schmid, Wolfgang (European University Viadrina) Date 2020 Abstract We consider the estimation of the multi-period optimal portfolio obtained by maximizing an exponential utility. Employing the Jeffreys non-informative prior and the conjugate informative prior, we derive stochastic representations for the optimal portfolio weights at each time point of portfolio reallocation. This provides a direct access not only to the posterior distribution of the portfolio weights but also to their point estimates together with uncertainties and their asymptotic distributions. Furthermore, we present the posterior predictive distribution for the investor's wealth at each time point of the investment period in terms of a stochastic representation for the future wealth realization. This in turn makes it possible to use quantile-based risk measures or to calculate the probability of default, i.e the probability of the investor wealth to become negative. We apply the suggested Bayesian approach to assess the uncertainty in the multi-period optimal portfolio by considering assets from the FTSE 100 in the weeks after the British referendum to leave the European Union. The behaviour of the novel portfolio estimation method in a precarious market situation is illustrated by calculating the predictive wealth, the risk associated with the holding portfolio, and the probability of default in each period. Subject Bayesian estimationCredible setsMulti-period optimal portfolioPosterior predictive distributionStochastic representation To reference this document use: http://resolver.tudelft.nl/uuid:24ab7661-a681-4b5a-9e69-b23a62bd1918 DOI https://doi.org/10.1016/j.jmva.2019.104544 Embargo date 2021-11-08 ISSN 0047-259X Source Journal of Multivariate Analysis, 175, 1-22 Bibliographical note Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. Part of collection Institutional Repository Document type journal article Rights © 2020 David Bauder, Taras Bodnar, N. Parolya, Wolfgang Schmid Files PDF 1_s2.0_S0047259X1930123X_main.pdf 808.86 KB Close viewer /islandora/object/uuid:24ab7661-a681-4b5a-9e69-b23a62bd1918/datastream/OBJ/view