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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…
Portfolio optimization is an important process in finance that consists in finding the optimal asset allocation that maximizes expected returns while minimizing risk. When assets are allocated in discrete units, this is a combinatorial…
This paper studies a type of periodic utility maximization problems for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on the relative ratio…
Mean-variance portfolio optimization problems often involve separable nonconvex terms, including penalties on capital gains, integer share constraints, and minimum position and trade sizes. We propose a heuristic algorithm for such problems…
A cardinality-constrained portfolio caps the number of stocks to be traded across and within groups or sectors. These limitations arise from real-world scenarios faced by fund managers, who are constrained by transaction costs and client…
We consider the problem of choosing a portfolio that maximizes the cumulative prospect theory (CPT) utility on an empirical distribution of asset returns. We show that while CPT utility is not a concave function of the portfolio weights, it…
We consider a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. We describe a framework for single-period optimization, where the trades in each period are found by solving a convex…
We introduce a solution scheme for portfolio optimization problems with cardinality constraints. Typical portfolio optimization problems are extensions of the classical Markowitz mean-variance portfolio optimization model. We solve such…
We propose an end-to-end distributionally robust system for portfolio construction that integrates the asset return prediction model with a distributionally robust portfolio optimization model. We also show how to learn the risk-tolerance…
A continuous-time financial portfolio selection model with expected utility maximization typically boils down to solving a (static) convex stochastic optimization problem in terms of the terminal wealth, with a budget constraint. In…
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…
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…
We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the objective function a penalty proportional to the…
We consider a trader who wants to direct his portfolio towards a set of acceptable wealths given by a convex risk measure. We propose a black-box algorithm, whose inputs are the joint law of stock prices and the convex risk measure, and…
We propose an alternative linearization to the classical Markowitz quadratic portfolio optimization model, based on maximum drawdown. This model, which minimizes maximum portfolio drawdown, is particularly appealing during times of…
We consider the terminal wealth utility maximization problem from the point of view of a portfolio manager who is paid by an incentive scheme, which is given as a convex function $g$ of the terminal wealth. The manager's own utility…
In this paper we consider a generalization of the Markowitz's Mean-Variance model under linear transaction costs and cardinality constraints. The cardinality constraints are used to limit the number of assets in the optimal portfolio. The…
Portfolio optimization involves selecting asset weights to minimize a risk-reward objective, such as the portfolio variance in the classical minimum-variance framework. Sparse portfolio selection extends this by imposing a cardinality…
This paper considers the finite horizon portfolio rebalancing problem in terms of mean-variance optimization, where decisions are made based on current information on asset returns and transaction costs. The study's novelty is that the…
In this paper, we consider the basic problem of portfolio construction in financial engineering, and analyze how market-based and analytical approaches can be combined to obtain efficient portfolios. As a first step in our analysis, we…