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The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone…
The portfolio optimization problem is a basic problem of financial analysis. In the study, an optimization model for constructing an options portfolio with a certain payoff function has been proposed. The model is formulated as an integer…
We study problems arising in real-time auction markets, common in e-commerce and computational advertising, where bidders face the problem of calculating optimal bids. We focus upon a contract management problem where a demand aggregator is…
The minimum (worst case) value of a long-only portfolio of bonds, over a convex set of yield curves and spreads, can be estimated by its sensitivities to the points on the yield curve. We show that sensitivity based estimates are…
Given an infeasible, unbounded, or pathological convex optimization problem, a natural question to ask is: what is the smallest change we can make to the problem's parameters such that the problem becomes solvable? In this paper, we address…
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…
We study a continuous-time portfolio optimization problem under an explicit constraint on the Deviation Conditional Value-at-Risk (DCVaR), defined as the difference between the CVaR and the expected terminal wealth. While the mean-CVaR…
Portfolio selection involves optimizing simultaneously financial goals such as risk, return and Sharpe ratio. This problem holds considerable importance in economics. However, little has been studied related to the nonconvexity of the…
We consider the problem of selecting a portfolio of assets that provides the investor a suitable balance of expected return and risk. With respect to the seminal mean-variance model of Markowitz, we consider additional constraints on the…
The sparse portfolio selection problem is one of the most famous and frequently-studied problems in the optimization and financial economics literatures. In a universe of risky assets, the goal is to construct a portfolio with maximal…
Funds at large portfolio management firms may consist of many portfolio managers (PMs), each managing a portion of the fund and optimizing a distinct objective. Although the PMs determine their trades independently, the trade lists may be…
Risk aversion plays a significant and central role in investors' decisions in the process of developing a portfolio. In this framework of portfolio optimization we determine the portfolio that possesses the minimal risk by using a new…
A highly relevant problem of modern finance is the design of Value-at-Risk (VaR) optimal portfolios. Due to contemporary financial regulations, banks and other financial institutions are tied to use the risk measure to control their credit,…
This paper studies a robust continuous-time Markowitz portfolio selection pro\-blem where the model uncertainty carries on the covariance matrix of multiple risky assets. This problem is formulated into a min-max mean-variance problem over…
We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in…
Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean…
We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption-investment strategy by studying the associated quadratic…
A fundamental problem in revenue management is to optimally choose the attributes of products, such that the total profit or revenue or market share is maximized. Usually, these attributes can affect both a product's market share…
Selecting the optimal Markowitz porfolio depends on estimating the covariance matrix of the returns of $N$ assets from $T$ periods of historical data. Problematically, $N$ is typically of the same order as $T$, which makes the sample…
Mean-reverting portfolios with few assets, but high variance, are of great interest for investors in financial markets. Such portfolios are straightforwardly profitable because they include a small number of assets whose prices not only…