Title: Bayesian Inference of the Multi-Period Optimal Portfolio for an Exponential Utility,
Abstract: We consider the estimation of the multi-period optimal portfolio obtained by
maximizing an exponential utility. Employing 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. 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
default probability in each period.