Minimum Rényi entropy portfolios

Lassance, Nathan; Vrins, Frédéric

doi:10.1007/s10479-019-03364-2

Cited by 24 publications

(14 citation statements)

References 65 publications

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“…The portfolio entropy minimization method (entropy as a risk): (i) It does not require the normality assumption; (ii) it can accommodate asymmetric distributions; (iii) it is fully non-parametric. See Philippatos (1972) [ 11 ], Jiang (2018) [ 39 ], and Lassance (2019) [ 40 ]—further discussion in Section 2.3 .…”

Section: Modern Portfolio Theorymentioning

confidence: 99%

“…Lastly, the third method assumes some probability distributions, but is not applicable for unknown distributions or non-parametric approaches. Other measures of entropy, such as Rényi entropy (1960) [ 43 ], have been explored by Lassance (2019) [ 40 ], but involve similar reliance on a non-parametric estimator of the exponential Rényi entropy function.…”

Section: Modern Portfolio Theorymentioning

confidence: 99%

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An Entropy-Based Approach to Portfolio Optimization

Mercurio

Xie

2020

Entropy

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This paper presents an improved method of applying entropy as a risk in portfolio optimization. A new family of portfolio optimization problems called the return-entropy portfolio optimization (REPO) is introduced that simplifies the computation of portfolio entropy using a combinatorial approach. REPO addresses five main practical concerns with the mean-variance portfolio optimization (MVPO). Pioneered by Harry Markowitz, MVPO revolutionized the financial industry as the first formal mathematical approach to risk-averse investing. REPO uses a mean-entropy objective function instead of the mean-variance objective function used in MVPO. REPO also simplifies the portfolio entropy calculation by utilizing combinatorial generating functions in the optimization objective function. REPO and MVPO were compared by emulating competing portfolios over historical data and REPO significantly outperformed MVPO in a strong majority of cases.

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Section: Modern Portfolio Theorymentioning

confidence: 99%

Section: Modern Portfolio Theorymentioning

confidence: 99%

An Entropy-Based Approach to Portfolio Optimization

Mercurio

Xie

2020

Entropy

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“…Many progresses have been made in exploring entropy of the portfolio weights as a maximization objective to encourage diversification levels ([ 31 , 32 , 33 , 34 , 35 , 36 , 37 ]). Lassance [ 38 ] used the R

nyi entropy discussed the portfolio optimization. For a detailed review of the application of entropy, please see [ 39 ].…”

Section: Introductionmentioning

confidence: 99%

Maximum Varma Entropy Distribution with Conditional Value at Risk Constraints

Liu

Chang

2020

Entropy

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It is well known that Markowitz’s mean-variance model is the pioneer portfolio selection model. The mean-variance model assumes that the probability density distribution of returns is normal. However, empirical observations on financial markets show that the tails of the distribution decay slower than the log-normal distribution. The distribution shows a power law at tail. The variance of a portfolio may also be a random variable. In recent years, the maximum entropy method has been widely used to investigate the distribution of return of portfolios. However, the mean and variance constraints were still used to obtain Lagrangian multipliers. In this paper, we use Conditional Value at Risk constraints instead of the variance constraint to maximize the entropy of portfolios. Value at Risk is a financial metric that estimates the risk of an investment. Value at Risk measures the level of financial risk within a portfolio. The metric is most commonly used by investment bank to determine the extent and occurrence ratio of potential losses in portfolios. Value at Risk is a single number that indicates the extent of risk in a given portfolio. This makes the risk management relatively simple. The Value at Risk is widely used in investment bank and commercial bank. It has already become an accepted standard in buying and selling assets. We show that the maximum entropy distribution with Conditional Value at Risk constraints is a power law. Algebraic relations between the Lagrangian multipliers and Value at Risk constraints are presented explicitly. The Lagrangian multipliers can be fixed exactly by the Conditional Value at Risk constraints.

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“…Huang [16] considers the credibility applying the mean-variance model and mean-semivariance model to proportional entropy fuzzy portfolios, as well as the clear form of the corresponding model. Lassance and Vrins [17] accurately quantify the uncertainty embedded in a distribution using a target function that depends on the R´enyi entropy index and considers the high-order moments. e portfolio generates a number of minimum variance combinations that are superior to the prior settings by minimizing the R´enyi entropy in terms of the risk-working capital trade closure.…”

Section: Introductionmentioning

confidence: 99%

Research on Probability Mean-Lower Semivariance-Entropy Portfolio Model with Background Risk

Gao

Sun

2020

Mathematical Problems in Engineering

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In the financial market, investors must deal with uncertain risk, and they also face background risk and many uncertain factors caused by their own characteristics. Considering the fuzzy nature of these factors as well as investors’ risk preferences, transaction costs, and so on, in order to reduce investment risk, an improved probability entropy measure is introduced, and a probability mean-lower semivariance-entropy model with different risk attitudes is established by using fuzzy sets and probability theory. To solve the portfolio model, an improved differential evolution algorithm is proposed and a numerical example is given. The numerical results show that the proposed algorithm is effective and that the model can disperse the financial risk to a certain extent and reasonably solve the portfolio problem under many different conditions.

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Minimum Rényi entropy portfolios

Cited by 24 publications

References 65 publications

An Entropy-Based Approach to Portfolio Optimization

An Entropy-Based Approach to Portfolio Optimization

Maximum Varma Entropy Distribution with Conditional Value at Risk Constraints

Research on Probability Mean-Lower Semivariance-Entropy Portfolio Model with Background Risk

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