Related papers: Covariance Matrix Estimation under Total Positivit…
A sample covariance matrix $\boldsymbol{S}$ of completely observed data is the key statistic in a large variety of multivariate statistical procedures, such as structured covariance/precision matrix estimation, principal component analysis,…
Modern Portfolio Theory (MPT) prescribes how to maximise the return of an asset portfolio for a given level of risk. The optimal trade-off between return and variance defines the efficient frontier. Whether actual cryptoasset portfolios…
In portfolio analysis, the traditional approach of replacing population moments with sample counterparts may lead to suboptimal portfolio choices. I show that optimal portfolio weights can be estimated using a machine learning (ML)…
We consider the problem of estimating high-dimensional covariance matrices of $K$-populations or classes in the setting where the sample sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a…
We propose a novel portfolio selection approach that manages to ease some of the problems that characterise standard expected utility maximisation. The optimal portfolio is no longer defined as the extremum of a suitably chosen utility…
Estimation error has plagued quantitative finance since Harry Markowitz launched modern portfolio theory in 1952. Using random matrix theory, we characterize a source of bias in the sample eigenvectors of financial covariance matrices.…
Minimum-variance portfolio optimizations rely on accurate covariance estimator to obtain optimal portfolios. However, it usually suffers from large error from sample covariance matrix when the sample size $n$ is not significantly larger…
Obtaining reliable estimates of conditional covariance matrices is an important task of heteroskedastic multivariate time series. In portfolio optimization and financial risk management, it is crucial to provide measures of uncertainty and…
Asset allocation is an investment strategy that aims to balance risk and reward by constantly redistributing the portfolio's assets according to certain goals, risk tolerance, and investment horizon. Unfortunately, there is no simple…
In this paper, we propose a market model with returns assumed to follow a multivariate normal tempered stable distribution defined by a mixture of the multivariate normal distribution and the tempered stable subordinator. This distribution…
In this paper, the mean-variance portfolio selection problem with Poisson jumps are studied, where the recursive utility is given by the solution to a backward stochastic differential equation with Poisson jumps. Both the maximum principle…
The focal point of this paper is the issue of "drawdown" which arises in recursive betting scenarios and related applications in the stock market. Roughly speaking, drawdown is understood to mean drops in wealth over time from peaks to…
The portfolio optimization problem in which the variances of the return rates of assets are not identical is analyzed in this paper using the methodology of statistical mechanical informatics, specifically, replica analysis. We define two…
A continuous-time Markowitz's mean-variance portfolio selection problem is studied in a market with one stock, one bond, and proportional transaction costs. This is a singular stochastic control problem,inherently in a finite time horizon.…
Portfolio optimization methods suffer from a catalogue of known problems, mainly due to the facts that pair correlations of asset returns are unstable, and that extremal risk measures such as maximum drawdown are difficult to predict due to…
Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance data. The covariance matrix reveals marginal correlations…
In this paper, we propose a novel variable selection approach in the framework of multivariate linear models taking into account the dependence that may exist between the responses. It consists in estimating beforehand the covariance matrix…
We analyze the problem of maximum likelihood estimation for Gaussian distributions that are multivariate totally positive of order two (MTP2). By exploiting connections to phylogenetics and single-linkage clustering, we give a simple proof…
This paper is concerned with portfolio optimization models for creating high-quality lists of recommended items to balance the accuracy and diversity of recommendations. However, the statistics (i.e., expectation and covariance of ratings)…
Changes in market conditions present challenges for investors as they cause performance to deviate from the ranges predicted by long-term averages of means and covariances. The aim of conditional asset allocation strategies is to overcome…