Related papers: A General Framework for Portfolio Theory. Part I: …
Classical mean-variance portfolio theory tells us how to construct a portfolio of assets which has the greatest expected return for a given level of return volatility. Utility theory then allows an investor to choose the point along this…
Volatility, as a primary indicator of financial risk, forms the foundation of classical frameworks such as Markowitz's Portfolio Theory and the Efficient Market Hypothesis (EMH). However, its conventional use rests on assumptions-most…
Portfolio selection problems that optimize expected utility are usually difficult to solve. If the number of assets in the portfolio is large, such expected utility maximization problems become even harder to solve numerically. Therefore,…
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…
In this paper, we propose a market model with returns assumed to follow a multivariate normal tempered stable distribution defined by a mixture of the multivariate normal distribution and the tempered stable subordinator. This distribution…
While investment funds publicly disclose their objectives in broad terms, their managers optimize for complex combinations of competing goals that go beyond simple risk-return trade-offs. Traditional approaches attempt to model this through…
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…
Portfolio managers often evaluate performance relative to benchmark, usually taken to be the Standard & Poor 500 stock index fund. This relative portfolio wealth is defined as the absolute portfolio wealth divided by wealth from investing…
We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate…
Markowitz's celebrated mean--variance portfolio optimization theory assumes that the means and covariances of the underlying asset returns are known. In practice, they are unknown and have to be estimated from historical data. Plugging the…
A new framework for portfolio diversification is introduced which goes beyond the classical mean-variance approach and portfolio allocation strategies such as risk parity. It is based on a novel concept called portfolio dimensionality 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…
This paper is devoted to study the optimal portfolio problem. Harry Markowitz's Ph.D. thesis prepared the ground for the mathematical theory of finance. In modern portfolio theory, we typically find asset returns that are modeled by a…
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…
We study Spectral Measures of Risk from the perspective of portfolio optimization. We derive exact results which extend to general Spectral Measures M_phi the Pflug--Rockafellar--Uryasev methodology for the minimization of alpha--Expected…
The classical mean-variance framework characterizes portfolio risk solely through return variance and the covariance matrix, implicitly assuming that all relevant sources of risk are captured by second moments. In modern financial markets,…
In finance industry portfolio construction deals with how to divide the investors' wealth across an asset-classes' menu in order to maximize the investors' gain. Main approaches in use at the present are based on variations of the classical…
We revisit the problem of portfolio selection, where an investor maximizes utility subject to a risk constraint. Our framework is very general and accommodates a wide range of utility and risk functionals, including non-concave utilities…
Portfolio optimization is a task that investors use to determine the best allocations for their investments, and fund managers implement computational models to help guide their decisions. While one of the most common portfolio optimization…
Investment approaches in financial instruments have been varied and often produce unpredictable results. Many investors in the earlier days of investment banking suffered catastrophical losses due to poor strategy and lack of understanding…