Optimization of a Long-Short Portfolio under Nonconvex Transaction Cost

Konno, Hiroshi; Akishino, Keisuke; Yamamoto, Rei

doi:10.1007/s10589-005-2056-5

Cited by 36 publications

(18 citation statements)

References 14 publications

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“…Gaivoronski and Pflug (2005) uses VaR as risk measure and introduces/sets forth mean-VaR frontiers. Konno et al (2005) present a branch and bound algorithm for constructing or rebalancing a portfolio and use absolute deviations of returns rates. Yao et al (2006) solve the index tracking problem with a portfolio containing only few assets.…”

Section: Introductionmentioning

confidence: 99%

A Robust Optimization Approach for Index Tracking Problem

Gharakhani¹,

Fazlelahi²,

Sadjadi³

2014

Journal of Computer Science

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Index tracking is an investment approach where the primary objective is to keep portfolio return as close as possible to a target index without purchasing all index components. The main purpose is to minimize the tracking error between the returns of the selected portfolio and a benchmark. In this study, quadratic as well as linear models are presented for minimizing the tracking error. The uncertainty is considered in the input data using a tractable robust framework that controls the level of conservatism while maintaining linearity. The linearity of the proposed robust optimization models allows a simple implementation of an ordinary optimization software package to find the optimal robust solution. The proposed model of this study employs Morgan Stanley Capital International Index as the target index and the results are reported for six national indices including Japan, the USA, the UK, Germany, Switzerland and France. The performance of the proposed models is evaluated using several financial criteria e.g., information ratio, market ratio, Sharpe ratio and Treynor ratio. The preliminary results demonstrate that the proposed model lowers the amount of tracking error while raising values of portfolio performance measures.

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Section: Introductionmentioning

confidence: 99%

A Robust Optimization Approach for Index Tracking Problem

Gharakhani¹,

Fazlelahi²,

Sadjadi³

2014

Journal of Computer Science

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“…Actually, this sim plifies the mathematical exposition, and every probability space admits a discrete approximation which achieves as much accuracy as needed. Many actuarial and financial analyses deal with discrete probability spaces (see Benati, 2003;Konno et al, 2005;Mansini et al, 2007, or Miller andRuszczynski, 2008, among many others), since this is not a restriction in practice. The proposed optimal reinsurance problem seems to be quite flexible and general, since it allows us to incorporate many particular situations such as bud get constraints, the maximization of the insurer expected wealth, etc.…”

Section: Introductionmentioning

confidence: 99%

Stable solutions for optimal reinsurance problems involving risk measures

Balbás

Heras

2011

European Journal of Operational Research

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a b s t r a c tThe optimal reinsurance problem is a classic topic in actuarial mathematics. Recent approaches consider a coherent or expectation bounded risk measure and minimize the global risk of the ceding company under adequate constraints. However, there is no consensus about the risk measure that the insurer must use, since every risk measure presents advantages and shortcomings when compared with others.This paper deals with a discrete probability space and analyzes the stability of the optimal reinsurance with respect to the risk measure that the insurer uses. We will demonstrate that there is a ''stable optimal retention'' that will show no sensitivity, insofar as it will solve the optimal reinsurance problem for many risk measures, thus providing a very robust reinsurance plan. This stable optimal retention is a stop loss contract, and it is easy to compute in practice. A fast linear time algorithm will be given and a numerical example presented.

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“…This justifies that many authors consider the absolute deviation in portfolio selection problems. For instance, Konno et al (2005), who can reduce the optimization problem to a linear one because they consider discrete return distributions (generated from recent samples).…”

Section: Introductionmentioning

confidence: 99%

“…For instance, this is done by Fö llmer and Schied (2002) and Nakano (2004). As said above, Konno et al (2005) can deal with a linear problem, but they minimize a particular dispersion and involve discrete returns. Benati (2003) also uses discrete sample-linked returns and gets other linear problem (that he combines with an integer fractional problem) to optimize the ''worst conditional expectation'', a coherent measure introduced in Artzner et al (1999).…”

Section: Introductionmentioning

confidence: 99%

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Portfolio choice and optimal hedging with general risk functions: A simplex-like algorithm

Balbás

Mayoral

2009

European Journal of Operational Research

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The minimization of general risk functions is becoming more and more important in portfolio choice theory and optimal hedging. There are two major reasons. Firstly, heavy tails and the lack of symmetry in the returns of many assets provokes that the classical opti mization of the standard deviation may lead to dominated strategies, from the point of view of the second order stochastic dominance. Secondly, but not less important, many institutional investors must respect legal capital requirements, which may be more easily studied if one deals with a risk measure related to capital losses. This paper proposes a new method to simultaneously minimize several general risk or dispersion measures. The representation the orems of risk functions are applied to transform the general risk minimization problem in a minimax problem, and later in a linear pro gramming problem between infinite dimensional Banach spaces. Then, new necessary and sufficient optimality conditions are stated and a simplex like algorithm is developed. The algorithm solves the dual problem and provides both optimal portfolios and their sensitivities.The approach is general enough and does not depend on any particular risk measure, but some of the most important cases are spe cially analyzed. A final real data numerical example illustrates the practical performance of the proposed methodology.

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Optimization of a Long-Short Portfolio under Nonconvex Transaction Cost

Cited by 36 publications

References 14 publications

A Robust Optimization Approach for Index Tracking Problem

A Robust Optimization Approach for Index Tracking Problem

Stable solutions for optimal reinsurance problems involving risk measures

Portfolio choice and optimal hedging with general risk functions: A simplex-like algorithm

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