Related papers: Dynamic Shrinkage Estimation of the High-Dimension…
The conventional wisdom of mean-variance (MV) portfolio theory asserts that the nature of the relationship between risk and diversification is a decreasing asymptotic function, with the asymptote approximating the level of portfolio…
In this paper, the optimal mean-reverting portfolio (MRP) design problem is considered, which plays an important role for the statistical arbitrage (a.k.a. pairs trading) strategy in financial markets. The target of the optimal MRP design…
Markowitz mean-variance portfolios with sample mean and covariance as input parameters feature numerous issues in practice. They perform poorly out of sample due to estimation error, they experience extreme weights together with high…
Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a…
Constrained approaches to maximum likelihood estimation in the context of finite mixtures of normals have been presented in the literature. A fully data-dependent constrained method for maximum likelihood estimation of clusterwise linear…
This work develops non-asymptotic theory for estimation of the long-run variance matrix and its inverse, the so-called precision matrix, for high-dimensional time series under general assumptions on the dependence structure including…
We develop a efficient, easy-to-implement, and strictly monotone numerical integration method for Mean-Variance (MV) portfolio optimization in realistic contexts, which involve jump-diffusion dynamics of the underlying controlled processes,…
In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal…
We consider the problem of choosing an optimal portfolio, assuming the asset returns have a Gaussian mixture (GM) distribution, with the objective of maximizing expected exponential utility. In this paper we show that this problem is…
This paper introduces a simple principle for robust high-dimensional statistical inference via an appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the moment conditions from sub-exponential…
Stochastic gradient descent (SGD) is perhaps the most prevalent optimization method in modern machine learning. Contrary to the empirical practice of sampling from the datasets without replacement and with (possible) reshuffling at each…
This paper proposes a robust, shocks-adaptive portfolio in a large-dimensional assets universe where the number of assets could be comparable to or even larger than the sample size. It is well documented that portfolios based on…
We find economically and statistically significant gains when using machine learning for portfolio allocation between the market index and risk-free asset. Optimal portfolio rules for time-varying expected returns and volatility are…
In this paper, we tackle the dynamic mean-variance portfolio selection problem in a {\it model-free} manner, based on (generative) diffusion models. We propose using data sampled from the real model $\mathbb P$ (which is unknown) with…
We derive an optimal shrinkage sample covariance matrix (SCM) estimator which is suitable for high dimensional problems and when sampling from an unspecified elliptically symmetric distribution. Specifically, we derive the optimal (oracle)…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
One of the goals in scaling sequential machine learning methods pertains to dealing with high-dimensional data spaces. A key related challenge is that many methods heavily depend on obtaining the inverse covariance matrix of the data. It is…
Many existing shrinkage approaches for time-varying parameter (TVP) models assume constant innovation variances across time points, inducing sparsity by shrinking these variances toward zero. However, this assumption falls short when states…
In this paper we consider the problem of minimising drawdown in a portfolio of financial assets. Here drawdown represents the relative opportunity cost of the single best missed trading opportunity over a specified time period. We formulate…
In this paper, we consider the portfolio optimization problem in a financial market under a general utility function. Empirical results suggest that if a significant market fluctuation occurs, invested wealth tends to have a notable change…