Related papers: Diversification quotients: Quantifying diversifica…
This paper addresses the problem of quantifying diversity for a set of objects. First, we conduct a systematic review of existing diversity measures and explore their undesirable behavior in certain cases. Based on this review, we formulate…
Entropy measures of probability distributions are widely used measures in ecology, biology, genetics, and in other fields, to quantify species diversity of a community. Unfortunately, entropy-based diversity indices, or diversity indices…
We review the recently introduced concept of variety of a financial portfolio and we sketch its importance for risk control purposes. The empirical behaviour of variety, correlation, exceedance correlation and asymmetry of the probability…
We propose a definition of diversification as a binary relationship between financial portfolios. According to it, a convex linear combination of several risk positions with some weights is considered to be less risky than the probabilistic…
Risk assessment under different possible scenarios is a source of uncertainty that may lead to concerning financial losses. We address this issue, first, by adapting a robust framework to the class of spectral risk measures. Second, we…
In this paper, we propose a novel axiomatic approach to evaluating the joint risk of multiple insurance risks under dependence uncertainty. Motivated by both the theory of expected utility and the Cobb-Dauglas utility function, we establish…
Diversification is the typical investment strategy of risk-averse agents. However, non-diversified positions that allocate all resources to a single asset, state of the world or revenue stream are common too. We show that whenever finitely…
Diversity indices are useful single-number metrics for characterizing a complex distribution of a set of attributes across a population of interest. The utility of these different metrics or sets of metrics depend on the context and…
Risk diversification is one of the dominant concerns for portfolio managers. Various portfolio constructions have been proposed to minimize the risk of the portfolio under some constrains including expected returns. We propose a portfolio…
Diversification is usually viewed as a reliable way to reduce risk, yet it can dramatically fail for heavy-tailed losses with infinite mean: pooling independent losses of this type may increase tail risk at every threshold. We study this…
The potential benefits of portfolio diversification have been known to investors for a long time. Markowitz (1952) suggested the seminal approach for optimizing the portfolio problem based on finding the weights as budget shares that…
This paper focuses on the developing of high-dimensional risk models to construct portfolios of securities in the US stock exchange. Investors seek to gain the highest profits and lowest risk in capital markets. We have developed various…
Risk control and optimal diversification constitute a major focus in the finance and insurance industries as well as, more or less consciously, in our everyday life. We present a discussion of the characterization of risks and of the…
Risk-only investment strategies have been growing in popularity as traditional in- vestment strategies have fallen short of return targets over the last decade. However, risk-based investors should be aware of four things. First,…
The investor is interested in the expected return and he is also concerned about the risk and the uncertainty assumed by the investment. One of the most popular concepts used to measure the risk and the uncertainty is the variance and/or…
This work proposes a unified framework for portfolio allocation, covering both asset selection and optimization, based on a multiple-hypothesis predict-then-optimize approach. The portfolio is modeled as a structured ensemble, where each…
Portfolio optimization methods have evolved significantly since Markowitz introduced the mean-variance framework in 1952. While the theoretical appeal of this approach is undeniable, its practical implementation poses important challenges,…
Uncertainty quantification (UQ) is crucial in machine learning, yet most (axiomatic) studies of uncertainty measures focus on classification, leaving a gap in regression settings with limited formal justification and evaluations. In this…
We propose a method for extending a given asset pricing formula to account for two additional sources of risk: the risk associated with future changes in market--calibrated parameters and the remaining risk associated with idiosyncratic…
We define and develop an approach for risk budgeting allocation - a risk diversification portfolio strategy - where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions…