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The main purpose of this study is the determination of the optimal length of the historical data for the estimation of statistical parameters in Markowitz Portfolio Optimization. We present a trading simulation using Markowitz method, for a…
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…
Recent studies stressed the fact that covariance matrices computed from empirical financial time series appear to contain a high amount of noise. This makes the classical Markowitz Mean-Variance Optimization model unable to correctly…
This paper presents how the most recent improvements made on covariance matrix estimation and model order selection can be applied to the portfolio optimisation problem. The particular case of the Maximum Variety Portfolio is treated but…
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 briefly review the approach to optimization of portfolios according to the theory of Markowitz and propose a further modification that can improve the outcome of the optimization process. The modification takes account of the entropic…
It is widely recognized that when classical optimal strategies are applied with parameters estimated from data, the resulting portfolio weights are remarkably volatile and unstable over time. The predominant explanation for this is the…
Classical portfolio optimization methods typically determine an optimal capital allocation through the implicit, yet critical, assumption of statistical time-invariance. Such models are inadequate for real-world markets as they employ…
We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that…
The Markowitz mean-variance portfolio optimization model aims to balance expected return and risk when investing. However, there is a significant limitation when solving large portfolio optimization problems efficiently: the large and dense…
We study a dynamic portfolio optimization problem related to convergence trading, which is an investment strategy that exploits temporary mispricing by simultaneously buying relatively underpriced assets and selling short relatively…
This paper derives an optimal portfolio that is based on trend-following signal. Building on an earlier related article, it provides a unifying theoretical setting to introduce an autocorrelation model with the covariance matrix of trends…
The portfolio optimisation problem, first raised by Harry Markowitz in 1952, has been a fundamental and central topic to understanding the stock market and making decisions. There has been plenty of works contributing to development of the…
This paper studies a portfolio optimization problem in a discrete-time Markovian model of a financial market, in which asset price dynamics depend on an external process of economic factors. There are transaction costs with a structure that…
In a fixed time horizon, appropriately executing a large amount of a particular asset -- meaning a considerable portion of the volume traded within this frame -- is challenging. Especially for illiquid or even highly liquid but also highly…
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…
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…
An investment portfolio consists of $n$ algorithmic trading strategies, which generate vectors of positions in trading assets. Sign opposite trades (buy/sell) cross each other as strategies are combined in a portfolio. Then portfolio…
We study Markowitz's mean-variance portfolio selection problem in a continuous-time Black-Scholes market with different borrowing and saving rates. The associated Hamilton-Jacobi-Bellman equation is fully nonlinear. Using a delicate partial…
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.…