Related papers: A General Framework for Portfolio Theory. Part I: …
It is shown that the axioms for coherent risk measures imply that whenever there is an asset in a portfolio that dominates the others in a given sample (which happens with finite probability even for large samples), then this portfolio…
The signal-noise ratio of a portfolio of p assets, its expected return divided by its risk, is couched as an estimation problem on the sphere. When the portfolio is built using noisy data, the expected value of the signal-noise ratio is…
We consider the problem of optimizing a portfolio of financial assets, where the number of assets can be much larger than the number of observations. The optimal portfolio weights require estimating the inverse covariance matrix of excess…
We present a framework for modeling asset and portfolio dynamics, incorporating this information into portfolio optimization. For this framework, we introduce the Commonality Principle, providing a solution for the optimal selection of…
The question of optimal portfolio is addressed. The conventional Markowitz portfolio optimisation is discussed and the shortcomings due to non-Gaussian security returns are outlined. A method is proposed to minimise the likelihood of…
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…
This paper studies a type of periodic utility maximization for portfolio management in an incomplete market model, where the underlying price diffusion process depends on some external stochastic factors. The portfolio performance is…
In this paper, the mean-variance portfolio selection problem with Poisson jumps are studied, where the recursive utility is given by the solution to a backward stochastic differential equation with Poisson jumps. Both the maximum principle…
The variance measures the portfolio risks the investors are taking. The investor, who holds his portfolio and doesn't trade his shares, at the current time can use the time series of the market trades that were made during the averaging…
We aim to construct a general framework for portfolio management in continuous time, encompassing both stocks and bonds. In these lecture notes we give an overview of the state of the art of optimal bond portfolios and we re-visit main…
The Markowitz model is still the cornerstone of modern portfolio theory. In particular, when focusing on the minimum-variance portfolio, the covariance matrix or better its inverse, the so-called precision matrix, is the only input…
This article develops a model that takes into account skewness risk in risk parity portfolios. In this framework, asset returns are viewed as stochastic processes with jumps or random variables generated by a Gaussian mixture distribution.…
We construct a deep portfolio theory. By building on Markowitz's classic risk-return trade-off, we develop a self-contained four-step routine of encode, calibrate, validate and verify to formulate an automated and general portfolio…
We analyze a nonlinear equation proposed by F. Black (1968) for the optimal portfolio function in a log-normal model. We cast it in terms of the risk tolerance function and provide, for general utility functions, existence, uniqueness and…
We give an algebraic definition of a Markowitz market and classify markets up to isomorphism. Given this classification, the theory of portfolio optimization in Markowitz markets without short selling constraints becomes trivial.…
This paper addresses the importance of incorporating various risk measures in portfolio management and proposes a dynamic hybrid portfolio optimization model that combines the spectral risk measure and the Value-at-Risk in the mean-variance…
Almost twenty years ago, E.R. Fernholz introduced portfolio generating functions which can be used to construct a variety of portfolios, solely in the terms of the individual companies' market weights. I. Karatzas and J. Ruf recently…
In this work, we introduce Modern Portfolio Theory using basic concepts from linear algebra, differential calculus, statistics, and optimization. This theory allows us to measure the return and risk of an investment portfolio, serving as a…
This work initiates research into the problem of determining an optimal investment strategy for investors with different attitudes towards the trade-offs of risk and profit. The probability distribution of the return values of the stocks…
Possibilistic risk theory starts from the hypothesis that risk is modelled by fuzzy numbers. In particular, in a possibilistic portfolio choice problem, the return of a risky asset will be a fuzzy number. The expected utility operators have…