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16
Comonotonic approximations for optimal portfolio selection problems
 Journal of Risk and Insurance
, 2005
"... We investigate multiperiod portfolio selection problems in a Black & Scholes type market where a basket of 1 riskfree and m risky securities are traded continuously. We look for the optimal allocation of wealth within the class of ’constant mix ’ portfolios. First, we consider the portfolio selectio ..."
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Cited by 26 (15 self)
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We investigate multiperiod portfolio selection problems in a Black & Scholes type market where a basket of 1 riskfree and m risky securities are traded continuously. We look for the optimal allocation of wealth within the class of ’constant mix ’ portfolios. First, we consider the portfolio selection problem of a decision maker who invests money at predetermined points in time in order to obtain a target capital at the end of the time period under consideration. A second problem concerns a decision maker who invests some amount of money (the initial wealth or provision) in order to be able to fullfil a series of future consumptions or payment obligations. Several optimality criteria and their interpretation within Yaari’s dual theory of choice under risk are presented. For both selection problems, we propose accurate approximations based on the concept of comonotonicity, as studied in Dhaene, Denuit, Goovaerts, Kaas & Vyncke (2002 a,b). Our analytical approach avoids simulation, and hence reduces the computing effort drastically. 1
SENSITIVITY ANALYSIS IN CONVEX QUADRATIC OPTIMIZATION: INVARIANT SUPPORT SET INTERVAL
, 2004
"... In sensitivity analysis one wants to know how the problem and the optimal solutions change under the variation of the input data. We consider the case when variation happens in the right hand side of the constraints and/or in the linear term of the objective function. We are interested to find the r ..."
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Cited by 4 (2 self)
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In sensitivity analysis one wants to know how the problem and the optimal solutions change under the variation of the input data. We consider the case when variation happens in the right hand side of the constraints and/or in the linear term of the objective function. We are interested to find the range of the parameter variation in Convex Quadratic Optimization (CQO) problems where the support set of a given primal optimal solution remains invariant. This question has been first raised in Linear Optimization (LO) and known as Type II (so called Support Set Invariancy) sensitivity analysis. We present computable auxiliary problems to identify the range of parameter variation in support set invariancy sensitivity analysis for CQO. It should be mentioned that all given auxiliary problems are LO problems and can be solved by an interior point method in polynomial time. We also highlight the differences between characteristics of support set invariancy sensitivity analysis for LO and CQO.
Downside Loss Aversion and Portfolio Management
, 2005
"... Downside loss averse preferences have seen a resurgence in the portfolio management literature. This is due to the increasing usage of derivatives in managing equity portfolios, and the increased usage of quantitative techniques for bond portfolio management. We employ the lower partial moment as ..."
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Cited by 3 (0 self)
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Downside loss averse preferences have seen a resurgence in the portfolio management literature. This is due to the increasing usage of derivatives in managing equity portfolios, and the increased usage of quantitative techniques for bond portfolio management. We employ the lower partial moment as a risk measure for downside loss aversion, and compare meanvariance (MV) and meanlower partial moment (MLPM) optimal portfolios under nonnormal asset return distributions. When asset returns are nearly normally distributed, there is little difference between the optimal MV and MLPM portfolios. When asset returns are nonnormal with large left tails, we document significant differences in MV and MLPM optimal portfolios. This observation is consistent with industry usage of MV theory for equity portfolios, but not for fixed income portfolios.
Global optimization of the scenario generation and portfolio selection problems. submitted
, 2006
"... Abstract. We consider the global optimization of two problems arising from financial applications. The first problem originates from the portfolio selection problem when highorder moments are taken into account. The second issue we address is the problem of scenario generation. Both problems are no ..."
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Cited by 2 (2 self)
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Abstract. We consider the global optimization of two problems arising from financial applications. The first problem originates from the portfolio selection problem when highorder moments are taken into account. The second issue we address is the problem of scenario generation. Both problems are nonconvex, largescale, and highly relevant in financial engineering. For the two problems we consider, we apply a new stochastic global optimization algorithm that has been developed specifically for this class of problems. The algorithm is an extension to the constrained case of the so called diffusion algorithm. We discuss how a financial planning model (of realistic size) can be solved to global optimality using a stochastic algorithm. Initial numerical results are given that show the feasibility of the proposed approach. 1
WeA16.1 Multistage Investments With Recourse: a SingleAsset Case with Transaction Costs
"... Abstract — We consider a financial decision problem involving dynamic investment decisions on a single risky instrument over multiple and discrete time periods. Investment returns are assumed stochastic and possibly dependent over time, and proportional transaction costs are considered in the model. ..."
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Cited by 2 (0 self)
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Abstract — We consider a financial decision problem involving dynamic investment decisions on a single risky instrument over multiple and discrete time periods. Investment returns are assumed stochastic and possibly dependent over time, and proportional transaction costs are considered in the model. In this setting, the investor’s goal is to determine investment policies that maximize the net profit while maintaining the associated risk under control. We propose approximations of the ensuing stochastic multistage optimization problem that are based on affine recourse strategies and that lead to efficiently solvable second order cone or semidefinite programs. I.
Dynamic modelling and optimization of nonmaturing accounts
, 2006
"... The risk management of nonmaturing account positions in a bank’s balance like savings deposits or certain types of loans is complicated by the embedded options that clients may exercise. In addition to the usual interest rate risk, there is also uncertainty in the timing and amount of future cash f ..."
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Cited by 1 (0 self)
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The risk management of nonmaturing account positions in a bank’s balance like savings deposits or certain types of loans is complicated by the embedded options that clients may exercise. In addition to the usual interest rate risk, there is also uncertainty in the timing and amount of future cash flows. Since the corresponding volume risk cannot directly be hedged, the account must be replicated by a portfolio of instruments with explicit maturities. This paper introduces a multistage stochastic programming model that determines an optimal replicating portfolio from scenarios for future outcomes of the relevant risk factors: Market rates, client rates and volume of the nonmaturing account. The weights for the allocation of new tranches are frequently adjusted to latest observations of the latter. A case study based on data of a real deposit position demonstrates that the resulting dynamic portfolio provides a significantly higher margin at lower risk compared to a static benchmark.
Robust Portfolio Selection Problems Including Uncertainty Factors
"... Abstract—This paper considers robust meanvariance portfolio selection problems including uncertainty sets and fuzzy factors. Since these problems are not welldefined problems due to fuzzy factors, it is hard to solve them directly. Therefore, introducing chance constraints, fuzzy goals and possibi ..."
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Abstract—This paper considers robust meanvariance portfolio selection problems including uncertainty sets and fuzzy factors. Since these problems are not welldefined problems due to fuzzy factors, it is hard to solve them directly. Therefore, introducing chance constraints, fuzzy goals and possibility measures, the proposed models are transformed into the deterministic equivalent problems. Furthermore, since it is difficult to solve them analytically and efficiently due to nonlinear programming problems, the solution method is constructed introducing a parameter and doing the equivalent transformations. Index Terms—Portfolio selection problem, Robust optimization, Fuzzy optimization, Nonlinear programming
Robust MeanVariance Portfolio Selection Problem Including Fuzzy Factors
"... Abstract—This paper considers robust meanvariance portfolio selection problems including uncertainty sets and fuzzy factors. Since these problems are not welldefined problems due to fuzzy factors, it is hard to solve them directly. Therefore, introducing chance constraints, fuzzy goals and possibi ..."
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Abstract—This paper considers robust meanvariance portfolio selection problems including uncertainty sets and fuzzy factors. Since these problems are not welldefined problems due to fuzzy factors, it is hard to solve them directly. Therefore, introducing chance constraints, fuzzy goals and possibility measures, the proposed models are transformed into the deterministic equivalent problems. Furthermore, since it is difficult to solve them analytically and efficiently due to nonlinear programming problems, the solution method is constructed introducing a parameter and doing the equivalent transformations. Index Terms—Portfolio selection problem, Robust optimization, Fuzzy optimization, Nonlinear programming
Forthcoming in Quarterly Review of Economics and Finance
, 2003
"... The mathematics of the portfolio frontier: ..."