scholarly journals Um Problema de Seleção de Carteiras de Múltiplos Períodos por Média e Variância

2005 ◽  
Vol 3 (1) ◽  
pp. 101
Author(s):  
Oswaldo Luiz do Valle Costa ◽  
Rodrigo De Barros Nabholz
Keyword(s):  
Optimization Problem ◽  
Expected Value ◽  
Expected Values ◽  
Mean Variance

In a recent paper, Li and Ng (2000) considered the multi-period mean variance optimization problem, with investing horizon T, for the case in which only the final variance Var(V(T)) or expected value of the portfolio E(V(T)) are considered in the optimization problem. In this paper we extend their results to the case in which the intermediate expected values E(V(t)) and variances Var(V(t)) for t = 1,,T can also be taken into account in the optimization problem. The main advantage of this technique is that it is possible to control the intermediate behavior of the portfolios return or variance. An example illustrating this situation is presented.

scholarly journals An Improvement of Stochastic Gradient Descent Approach for Mean-Variance Portfolio Optimization Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Stephanie S. W. Su ◽  
Sie Long Kek
Keyword(s):  
Portfolio Optimization ◽  
Standard Error ◽  
Gradient Descent ◽  
Optimization Problem ◽  
Stochastic Gradient Descent ◽  
Moment Estimation ◽  
The Mean ◽  
Portfolio Optimization Problem ◽  
Mean Variance Portfolio ◽  
Mean Variance

In this paper, the current variant technique of the stochastic gradient descent (SGD) approach, namely, the adaptive moment estimation (Adam) approach, is improved by adding the standard error in the updating rule. The aim is to fasten the convergence rate of the Adam algorithm. This improvement is termed as Adam with standard error (AdamSE) algorithm. On the other hand, the mean-variance portfolio optimization model is formulated from the historical data of the rate of return of the S&P 500 stock, 10-year Treasury bond, and money market. The application of SGD, Adam, adaptive moment estimation with maximum (AdaMax), Nesterov-accelerated adaptive moment estimation (Nadam), AMSGrad, and AdamSE algorithms to solve the mean-variance portfolio optimization problem is further investigated. During the calculation procedure, the iterative solution converges to the optimal portfolio solution. It is noticed that the AdamSE algorithm has the smallest iteration number. The results show that the rate of convergence of the Adam algorithm is significantly enhanced by using the AdamSE algorithm. In conclusion, the efficiency of the improved Adam algorithm using the standard error has been expressed. Furthermore, the applicability of SGD, Adam, AdaMax, Nadam, AMSGrad, and AdamSE algorithms in solving the mean-variance portfolio optimization problem is validated.

scholarly journals Reward Value Coding Distinct From Risk Attitude-Related Uncertainty Coding in Human Reward Systems

2007 ◽  
Vol 97 (2) ◽  
pp. 1621-1632 ◽  
Author(s):  
Philippe N. Tobler ◽  
John P. O'Doherty ◽  
Raymond J. Dolan ◽  
Wolfram Schultz
Keyword(s):  
Risk Aversion ◽  
Risk Attitude ◽  
Mean Value ◽  
Expected Value ◽  
Individual Risk ◽  
Functional Magnetic Resonance ◽  
Coding Regions ◽  
Monetary Rewards ◽  
Expected Values ◽  
Value Coding

When deciding between different options, individuals are guided by the expected (mean) value of the different outcomes and by the associated degrees of uncertainty. We used functional magnetic resonance imaging to identify brain activations coding the key decision parameters of expected value (magnitude and probability) separately from uncertainty (statistical variance) of monetary rewards. Participants discriminated behaviorally between stimuli associated with different expected values and uncertainty. Stimuli associated with higher expected values elicited monotonically increasing activations in distinct regions of the striatum, irrespective of different combinations of magnitude and probability. Stimuli associated with higher uncertainty (variance) elicited increasing activations in the lateral orbitofrontal cortex. Uncertainty-related activations covaried with individual risk aversion in lateral orbitofrontal regions and risk-seeking in more medial areas. Furthermore, activations in expected value-coding regions in prefrontal cortex covaried differentially with uncertainty depending on risk attitudes of individual participants, suggesting that separate prefrontal regions are involved in risk aversion and seeking. These data demonstrate the distinct coding in key reward structures of the two basic and crucial decision parameters, expected value, and uncertainty.

A MEAN–VARIANCE BOUND FOR A THREE-PIECE LINEAR FUNCTION

2007 ◽  
Vol 21 (4) ◽  
pp. 611-621 ◽  
Author(s):  
Karthik Natarajan ◽  
Zhou Linyi
Keyword(s):  
Convex Function ◽  
Closed Form ◽  
Linear Function ◽  
Upper Bound ◽  
Random Variable ◽  
Expected Value ◽  
Variance Bound ◽  
The Mean ◽  
Mean Variance

In this article, we derive a tight closed-form upper bound on the expected value of a three-piece linear convex function E[max(0, X, mX − z)] given the mean μ and the variance σ2 of the random variable X. The bound is an extension of the well-known mean–variance bound for E[max(0, X)]. An application of the bound to price the strangle option in finance is provided.

scholarly journals Fuzzy optimization for portfolio selection based on Embedding Theorem in Fuzzy Normed Linear Spaces

Organizacija ◽  
2014 ◽  
Vol 47 (2) ◽  
pp. 90-97 ◽  
Author(s):  
Farnaz Solatikia ◽  
Erdem Kiliç ◽  
Gerhard Wilhelm Weber
Keyword(s):  
Banach Space ◽  
Portfolio Selection ◽  
Optimization Problem ◽  
Fuzzy Optimization ◽  
Embedding Theorem ◽  
Fuzzy Decision Making ◽  
Normed Spaces ◽  
Open Set ◽  
Mean Variance ◽  
Fuzzy Banach Space

Abstract Background: This paper generalizes the results of Embedding problem of Fuzzy Number Space and its extension into a Fuzzy Banach Space C(Ω) × C(Ω), where C(Ω) is the set of all real-valued continuous functions on an open set Ω. Objectives: The main idea behind our approach consists of taking advantage of interplays between fuzzy normed spaces and normed spaces in a way to get an equivalent stochastic program. This helps avoiding pitfalls due to severe oversimplification of the reality. Method: The embedding theorem shows that the set of all fuzzy numbers can be embedded into a Fuzzy Banach space. Inspired by this embedding theorem, we propose a solution concept of fuzzy optimization problem which is obtained by applying the embedding function to the original fuzzy optimization problem. Results: The proposed method is used to extend the classical Mean-Variance portfolio selection model into Mean Variance-Skewness model in fuzzy environment under the criteria on short and long term returns, liquidity and dividends. Conclusion: A fuzzy optimization problem can be transformed into a multiobjective optimization problem which can be solved by using interactive fuzzy decision making procedure. Investor preferences determine the optimal multiobjective solution according to alternative scenarios.

scholarly journals MINIMAL VARIANCE HEDGING FOR INSIDER TRADING

2006 ◽  
Vol 09 (08) ◽  
pp. 1351-1375 ◽  
Author(s):  
FRANCESCA BIAGINI ◽  
BERNT ØKSENDAL
Keyword(s):  
Incomplete Markets ◽  
Insider Trading ◽  
Optimal Strategy ◽  
Explicit Solution ◽  
Expected Value ◽  
Enlargement Of Filtration ◽  
Minimal Variance ◽  
Mean Variance ◽  
Initial Enlargement Of Filtration

In this paper, we first study the problem of minimal hedging for an insider trader in incomplete markets. We use the forward integral in order to model the insider portfolio and consider a general larger filtration. We characterize the optimal strategy in terms of a martingale condition. In the second part we focus on a problem of mean-variance hedging where the insider tries to minimize the variance of his wealth at time T given that this wealth has a fixed expected value A. We solve this problem for an initial enlargement of filtration by providing an explicit solution.

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