Related papers: A General Framework for Portfolio Theory. Part I: …
We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio…
Monotone mean-variance (MMV) utility is the minimal modification of the classical Markowitz utility that respects rational ordering of investment opportunities. This paper provides, for the first time, a complete characterization of optimal…
Traditional Markowitz portfolio optimization constrains daily portfolio variance to a target value, optimising returns, Sharpe or variance within this constraint. However, this approach overlooks the relationship between variance at…
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…
Entropy based ideas find wide-ranging applications in finance for calibrating models of portfolio risk as well as options pricing. The abstracted problem, extensively studied in the literature, corresponds to finding a probability measure…
In his famous paper, Markowitz (1952) derived the dependence of portfolio random returns on the random returns of its securities. This result allowed Markowitz to obtain his famous expression for portfolio variance. We show that Markowitz's…
We review some fundamental concepts of investment from a mathematical perspective, concentrating specifically on fractional-Kelly portfolios, which allocate a fraction of wealth to a growth-optimal portfolio while the remainder collects (or…
The aim of this study is to present proofs for new theorems. Basic thoughts of new definitions emerge from the decision-making under uncertainty in economics and finance. Shape of the certain utility curve is central to standard definitions…
Finding an optimal balance between risk and returns in investment portfolios is a central challenge in quantitative finance, often addressed through Markowitz portfolio theory (MPT). While traditional portfolio optimization is carried out…
In portfolio optimization, decision makers face difficulties from uncertainties inherent in real-world scenarios. These uncertainties significantly influence portfolio outcomes in both classical and multi-objective Markowitz models. 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 study the problem of optimal long term portfolio selection with a view to beat a benchmark. Two kinds of objectives are considered. One concerns the probability of outperforming the benchmark and seeks either to minimise the decay rate…
In this paper we develop a concrete and fully implementable approach to the optimization of functionally generated portfolios in stochastic portfolio theory. The main idea is to optimize over a family of rank-based portfolios parameterized…
Obtaining utility maximizing optimal portfolios in closed form is a challenging issue when the return vector follows a more general distribution than the normal one. In this note, we give closed form expressions, in markets based on…
The fundamental principle in Modern Portfolio Theory (MPT) is based on the quantification of the portfolio's risk related to performance. Although MPT has made huge impacts on the investment world and prompted the success and prevalence of…
This paper proposes swaps on two important new measures of generalized variance, namely the maximum eigen-value and trace of the covariance matrix of the assets involved. We price these generalized variance swaps for financial markets with…
Given two random realized returns on an investment, which is to be preferred? This is a fundamental problem in finance that has no definitive solution except in the case one investment always returns more than the other. In 1952 Markowitz…
Consider an equity market with $n$ stocks. The vector of proportions of the total market capitalizations that belong to each stock is called the market weight. The market weight defines the market portfolio which is a buy-and-hold portfolio…
We consider a utility-maximization problem in a general semimartingale financial model, subject to constraints on the number of shares held in each risky asset. These constraints are modeled by predictable convex-set-valued processes whose…
Markowitz's optimal portfolio relies on the accurate estimation of correlations between asset returns, a difficult problem when the number of observations is not much larger than the number of assets. Using powerful results from random…