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Multiobjective quadratic programming problem: a priority based fuzzy goal programming
 International Journal of Computer Applications
"... Abstract: This paper presents fuzzy goal programming approach for solving multiobjective quadratic programming problem. The problem deals with a decisionmaking unit with multiple objective functions, which are quadratic in nature and the system constraints are linear functions. In the proposed appro ..."
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Abstract: This paper presents fuzzy goal programming approach for solving multiobjective quadratic programming problem. The problem deals with a decisionmaking unit with multiple objective functions, which are quadratic in nature and the system constraints are linear functions. In the proposed approach, we first formulate the quadratic membership functions by determining best solution of the objective functions subject to the system constraints. The quadratic membership functions are then linearized into equivalent linear membership functions at the best solution point by using first order Taylor polynomial series. Then fuzzy goal programming technique is used for solving the problem by minimizing only the negative deviational variables. A multiobjective quadratic programming problem is solved to demonstrate the efficiency of the proposed approach.
Unified Framework of MeanField Formulations for Optimal Multiperiod MeanVariance Portfolio Selection
, 2014
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OPTIMAL INVESTMENT WITH NOISE TRADING RISK∗
, 2008
"... Abstract This paper investigates the optimal dynamic investment for an investor who maximizes constant absolute risk aversion (CARA) utility in a discretetime market with a riskfree bond and a risky stock. The risky stock is assumed to present both the dividend risk and the price risk. With our ass ..."
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Abstract This paper investigates the optimal dynamic investment for an investor who maximizes constant absolute risk aversion (CARA) utility in a discretetime market with a riskfree bond and a risky stock. The risky stock is assumed to present both the dividend risk and the price risk. With our assumptions, the dividend risk is equivalent to fundamental risk, and the price risk is equivalent to the noise trading risk. The analytical expression for the optimal investment strategy is obtained by dynamic programming. The main result in this paper highlights the importance of differentiating between noise trading risk and fundamental risk for the optimal dynamic investment. Key words Dynamic investment, noise trade, overlapping generation, serial correlation. 1
OPTIMIZATION OF A FUTURES PORTFOLIO UTILIZING NUMERICAL MARKET PHASEDETECTION
"... Abstract. This paper presents an application of the recently developed method for simultaneous dimension reduction and metastability analysis of highdimensional time series in context of computational finance. Further extensions are included to combine statespecific principal component analysis ( ..."
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Abstract. This paper presents an application of the recently developed method for simultaneous dimension reduction and metastability analysis of highdimensional time series in context of computational finance. Further extensions are included to combine statespecific principal component analysis (PCA) and statespecific regressive trend models to handle the highdimensional, nonstationary data. The identification of market phases allows to control the involved phasespecific risk for futures portfolios. The numerical optimization strategy for futures portfolios based on the Tykhonovtype regularization is presented. The application of proposed strategies to online detection of the market phases is exemplified first on the simulated data, then on historical futures prices for oil and wheat between 20052008. Numerical tests demonstrate the comparison of the presented methods with existent approaches.
A discontinuous mispricing model under asymmetric information
, 2015
"... a b s t r a c t We study a discontinuous mispricing model of a risky asset under asymmetric information where jumps in the asset price and mispricing are modelled by Lévy processes. By contracting the filtration of the informed investor, we obtain optimal portfolios and maximum expected utilities f ..."
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a b s t r a c t We study a discontinuous mispricing model of a risky asset under asymmetric information where jumps in the asset price and mispricing are modelled by Lévy processes. By contracting the filtration of the informed investor, we obtain optimal portfolios and maximum expected utilities for the informed and uninformed investors. We also discuss their asymptotic properties, which can be estimated using the instantaneous centralized moments of return. We find that optimal and asymptotic utilities are increased due to jumps in mispricing for the uninformed investor but the informed investor still has excess utility, provided there is not too little or too much mispricing.
MeanVariance Portfolio Optimization: EigendecompositionBased Methods MeanVariance Portfolio Optimization: EigendecompositionBased Methods
"... Abstract Modern portfolio theory is about determining how to distribute capital among available securities such that, for a given level of risk, the expected return is maximized, or for a given level of return, the associated risk is minimized. In the pioneering work of Markowitz in 1952, variance ..."
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Abstract Modern portfolio theory is about determining how to distribute capital among available securities such that, for a given level of risk, the expected return is maximized, or for a given level of return, the associated risk is minimized. In the pioneering work of Markowitz in 1952, variance was used as a measure of risk, which gave rise to the wellknown meanvariance portfolio optimization model. Although other meanrisk models have been proposed in the literature, the meanvariance model continues to be the backbone of modern portfolio theory and it is still commonly applied. The scope of this thesis is a solution technique for the meanvariance model in which eigendecomposition of the covariance matrix is performed. The first part of the thesis is a review of the meanrisk models that have been suggested in the literature. For each of them, the properties of the model are discussed and the solution methods are presented, as well as some insight into possible areas of future research. The second part of the thesis is two research papers. In the first of these, a solution technique for solving the meanvariance problem is proposed. This technique involves making an eigendecomposition of the covariance matrix and solving an approximate problem that includes only relatively few eigenvalues and corresponding eigenvectors. The method gives strong bounds on the exact solution in a reasonable amount of computing time, and can thus be used to solve largescale meanvariance problems. The second paper studies the meanvariance model with cardinality constraints, that is, with a restricted number of securities included in the portfolio, and the solution technique from the first paper is extended to solve such problems. Nearoptimal solutions to largescale cardinality constrained meanvariance portfolio optimization problems are obtained within a reasonable amount of computing time, compared to the time required by a commercial generalpurpose solver. v Populärvetenskaplig sammanfattning För den som har kapital att investera kan det vara svårt att avgöra vilka investeringar som är mest fördelaktiga. Till stöd för beslutet kan matematiska modeller användas och denna avhandling handlar om hur man kan beräkna lösningar till sådana modeller. De investeringsalternativ som betraktas är finansiella instrument som är föremål för daglig handel, som aktier och obligationer. En investerare placerar kapital i finansiella instrument eftersom de förväntas ge en god avkastning över tiden. Samtidigt är sådana placeringar alltid förknippade med risktagande. Förväntad avkastning och risk varierar kraftigt mellan olika instrument. Till exempel ger placeringar i statsobligationer typiskt mycket låg avkastning till mycket låg risk, medan placeringar i aktier i nystartade bolag som utvecklar nya läkemedel kan ge mycket hög avkastning samtidigt som risken är mycket hög. Att investera kan ses som en avvägning mellan den förväntade avkastningen och den risk som investeringen innebär, och typiskt är hög förväntad avkastning också associerade med en hög risk, vilken kan leda till stora förluster. En rationell investerare vill undvika alltför stora risker, men för att investeringen ska bli rimligt lönsam måste en viss risk accepteras. För att minska den totala risken sprider en investerare normalt sitt kapital på en portfölj av finansiella instrument. Dock är vanligen avkastningarna för instrumenten i en portfölj inte oberoende av varandra, utan samvarierar. Till exempel kan alla bolag inom en och samma bransch förväntas ha likartade beroenden av den ekonomiska konjunkturen. Denna omständighet försvårar avsevärt problemet att sätta samman en portfölj. Instrumenten och de kapital som investeras i var och en av dem väljs så att både den samlade avkastningen och den samlade risken för portföljen blir acceptabel utifrån investerarens preferenser. Matematiska modeller som kan användas för att finna en portfölj av investeringar som är optimal med avseende på den önskade avvägningen mellan förväntad avkastning och risk med de investeringsalternativ som finns tillgängliga på marknaden är typiskt beräkningskrävande, samtidigt som man på kort tid vill kunna ta fram flera olika förslag på portföljer. I denna avhandling presenteras en ny typ av beräkningsmetoder som är bra på att ta fram optimala portföljer på kort tid. vii
Multiperiod fuzzy meansemi variance portfolio selection problem with transaction cost and minimum transaction lots using genetic algorithm
, 2016
"... Multiperiod models of portfolio selection have been developed in the literature with respect to certain assumptions. In this study, for the first time, the portfolio selection problem has been modeled based on meansemi variance with transaction cost and minimum transaction lots considering functi ..."
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Multiperiod models of portfolio selection have been developed in the literature with respect to certain assumptions. In this study, for the first time, the portfolio selection problem has been modeled based on meansemi variance with transaction cost and minimum transaction lots considering functional constraints and fuzzy parameters. Functional constraints such as transaction cost and minimum transaction lots were included. In addition, the returns on assets parameters were considered as trapezoidal fuzzy numbers. An efficient genetic algorithm (GA) was designed, results were analyzed using numerical instances and sensitivity analysis were executed. In the numerical study, the problem was solved based on the presence or absence of each mode of constraints including transaction costs and minimum transaction lots. In addition, with the use of sensitivity analysis, the results of the model were presented with the variations of minimum expected rate of programming periods.
On the Equivalence of Quadratic Optimization Problems Commonly Used in Portfolio Theory
"... In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz meanvariance problem as well as the problems based on the meanvariance utility function and the quadratic utility. Conditions are derived under which the solutions o ..."
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In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz meanvariance problem as well as the problems based on the meanvariance utility function and the quadratic utility. Conditions are derived under which the solutions of these three optimization procedures coincide and are lying on the efficient frontier, the set of meanvariance optimal portfolios. It is shown that the solutions of the Markowitz optimization problem and the quadratic utility problem are not always meanvariance efficient. The conditions for the meanvariance efficiency of the solutions depend on the unknown parameters of the asset returns. We deal with the problem of parameter uncertainty in detail and derive the probabilities that the estimated solutions of the Markowitz problem and the quadratic utility problem are meanvariance efficient. Because these probabilities deviate from one the above mentioned quadratic optimization problems are not stochastically equivalent. The obtained results are illustrated by an empirical study.
A ClosedForm Solution of the MultiPeriod Portfolio Choice Problem for a Quadratic Utility Function
"... In the present paper, we derive a closedform solution of the multiperiod portfolio choice problem for a quadratic utility function with and without a riskless asset. All results are derived under weak conditions on the asset returns. No assumption on the correlation structure between different tim ..."
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In the present paper, we derive a closedform solution of the multiperiod portfolio choice problem for a quadratic utility function with and without a riskless asset. All results are derived under weak conditions on the asset returns. No assumption on the correlation structure between different time points is needed and no assumption on the distribution is imposed. All expressions are presented in terms of the conditional mean vectors and the conditional covariance matrices. If the multivariate process of the asset returns is independent it is shown that in the case without a riskless asset the solution is presented as a sequence of optimal portfolio weights obtained by solving the singleperiod Markowitz optimization problem. The process dynamics are included only in the shape parameter of the utility function. If a riskless asset is present then the multiperiod optimal portfolio weights are proportional to the singleperiod solutions multiplied by timevarying constants which are depending on the process dynamics. Remarkably, in the case of a portfolio selection with the tangency portfolio the multiperiod solution coincides with the sequence of the simpleperiod solutions. Finally, we compare the suggested strategies with existing multiperiod portfolio allocation methods for real data.
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"... Noname manuscript No. (will be inserted by the editor) Robust optimal strategies for an insurer with reinsurance and investment under benchmark and meanvariance criteria ..."
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Noname manuscript No. (will be inserted by the editor) Robust optimal strategies for an insurer with reinsurance and investment under benchmark and meanvariance criteria