In this paper, we propose the test for the location of the tangency portfolio on the set of feasible portfolios when both the population and the sample covariance matrices of asset returns are singular. We derive the exact distribution of the test statistic under both the null and alternative...

In this paper we consider the product of a singular Wishart random matrix and a singular normal random vector. A very useful stochastic representation is derived for this product, in using which the characteristic function of the product and its asymptotic distribution under the double...

In this paper, we study the distributional properties of the tangency portfolio (TP) weights assuming a normal distribution of the logarithmic returns. We derive a stochastic representation of the TP weights that fully describes their distribution. Under a high-dimensional asymptotic regime,...

This article presents a comprehensive study on developing a predictive product pricing model using LightGBM, a machine learning method optimized for regression challenges in situations with limited historical data. It begins by detailing the core principles of LightGBM, including decision trees,...

This article presents a comprehensive study on developing a predictive product pricing model using LightGBM, a machine learning method optimized for regression challenges in situations with limited historical data. It begins by detailing the core principles of LightGBM, including decision trees,...

In this paper, we extend the standard Gaussian stochastic-volatility Bayesian VAR by employing the generalized hyperbolic skew Student's t distribution for the innovations. Allowing the skewness parameter to vary over time, our specification permits flexible modelling of innovations in terms of...

This paper examines optimal portfolio selection using quantile-based risk measures such as Valueat-Risk (VaR) and Conditional Value-at-Risk (CVaR). We address the case of a singular covariance matrix of asset returns, which leads to an optimization problem with infinitely many solutions. An...

Multivariate random sums appear in many scientific fields, most notably in actuarial science, where they model both the number of claims and their sizes. Unfortunately, they pose severe inferential problems. For example, their density function is analytically intractable, in the general case,...

There is considerable literature on matrix-variate gamma distributions, also known as Wishart distributions, which are driven by a shape parameter with values in the (Gindikin) set {i/2, i = 1, . . . , k−1}∪((k−1)/2, É). We provide an extension of this class to the case where the shape...

In the paper we consider the optimal portfolio choice problem under parameter uncertainty when the covariance matrix of asset returns is singular. Very useful stochastic representations are deduced for the characteristics of the expected utility optimal portfolio. Using these stochastic...