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Proximal distance algorithms combine the classical penalty method of constrained minimization with distance majorization. If $f(\boldsymbol{x})$ is the loss function, and $C$ is the constraint set in a constrained minimization problem, then…
We consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk…
Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…
The least squares Monte Carlo algorithm has become popular for solving portfolio optimization problems. A simple approach is to approximate the value functions on a discrete grid of portfolio weights, then use control regression to…
Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…
This research proposes an enhancement to the innovative portfolio optimization approach using the G-Learning algorithm, combined with parametric optimization via the GIRL algorithm (G-learning approach to the setting of Inverse…
We propose a new unified framework for describing and designing gradient-based convex optimization methods from a numerical analysis perspective. There the key is the new concept of weak discrete gradients (weak DGs), which is a…
In this paper, we propose a sparse equity portfolio optimization (SEPO) based on the mean-variance portfolio selection model. Aimed at minimizing transaction cost by avoiding small investments, this new model includes $\ell_0$-norm…
A new variant of Newton's method for empirical risk minimization is studied, where at each iteration of the optimization algorithm, the gradient and Hessian of the objective function are replaced by robust estimators taken from existing…
We consider the problem of the statistical uncertainty of the correlation matrix in the optimization of a financial portfolio. We show that the use of clustering algorithms can improve the reliability of the portfolio in terms of the ratio…
Markowitz' celebrated optimal portfolio theory generally fails to deliver out-of-sample diversification. In this note, we propose a new portfolio construction strategy based on symmetry arguments only, leading to "Eigenrisk Parity"…
In this paper, we revisit the relationship between investors' utility functions and portfolio allocation rules. We derive portfolio allocation rules for asymmetric Laplace distributed $ALD(\mu,\sigma,\kappa)$ returns and compare them with…
More than seventy years ago Harry Markowitz formulated portfolio construction as an optimization problem that trades off expected return and risk, defined as the standard deviation of the portfolio returns. Since then the method has been…
Stock portfolio optimization is the process of constant re-distribution of money to a pool of various stocks. In this paper, we will formulate the problem such that we can apply Reinforcement Learning for the task properly. To maintain a…
The question of optimal portfolio is addressed. The conventional Markowitz portfolio optimisation is discussed and the shortcomings due to non-Gaussian security returns are outlined. A method is proposed to minimise the likelihood of…
We consider the classic Kelly gambling problem with general distribution of outcomes, and an additional risk constraint that limits the probability of a drawdown of wealth to a given undesirable level. We develop a bound on the drawdown…
Strategic asset allocation requires an investor to select stocks from a given basket of assets. The perspective of our investor is to maximize risk-adjusted alpha returns relative to a benchmark index. Historical returns are used to provide…
We study the design of portfolios under a minimum risk criterion. The performance of the optimized portfolio relies on the accuracy of the estimated covariance matrix of the portfolio asset returns. For large portfolios, the number of…
The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…
This paper aims to develop new mathematical and computational tools for modeling the distribution of portfolio returns across portfolios. We establish relevant mathematical formulas and propose efficient algorithms, drawing upon powerful…