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24
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 sele ..."
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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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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.
An affine control method for optimal dynamic asset allocation with transaction costs
 SIAM Journal on Control and Optimization
"... Abstract. In this paper, we present a novel and computationally efficient approach to constrained discretetime dynamic asset allocation over multiple periods. This technique is able to control portfolio expectation and variance at both final and intermediate stages of the decision horizon and may a ..."
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Abstract. In this paper, we present a novel and computationally efficient approach to constrained discretetime dynamic asset allocation over multiple periods. This technique is able to control portfolio expectation and variance at both final and intermediate stages of the decision horizon and may account for proportional transaction costs and intertemporal dependence of the return process. A key feature of the proposed method is the use of a linearly parameterized class of feedback control policies, which permits us to obtain explicit analytic expressions for the portfolio statistics over time. These expressions are proved to be convex in the decision parameters, and hence, under these control laws, the multistage problem is formulated and solved by means of efficient tools for quadratic or secondordercone convex programming.
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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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.
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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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.
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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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
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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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.
Modeling and optimization of risk
 Surveys in Operations Research and Management Science
"... This paper surveys the most recent advances in the context of decision making under uncertainty, with an emphasis on the modeling of riskaverse preferences using the apparatus of axiomatically defined risk functionals, such as coherent measures of risk and deviation measures, and their connection t ..."
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This paper surveys the most recent advances in the context of decision making under uncertainty, with an emphasis on the modeling of riskaverse preferences using the apparatus of axiomatically defined risk functionals, such as coherent measures of risk and deviation measures, and their connection to utility theory, stochastic dominance, and other more established methods.
A NONLINEAR CONTROL POLICY USING KERNEL METHOD FOR DYNAMIC ASSET ALLOCATION
, 2011
"... Abstract We build a computational framework for determining an optimal dynamic asset allocation over multiple periods. To do this, we use a nonlinear control policy, which is a function of past returns of investable assets. By employing a kernel method, the problem of selecting the best control poli ..."
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Abstract We build a computational framework for determining an optimal dynamic asset allocation over multiple periods. To do this, we use a nonlinear control policy, which is a function of past returns of investable assets. By employing a kernel method, the problem of selecting the best control policy from among nonlinear functions can be formulated as a convex quadratic optimization problem. Furthermore, we reduce the problem to a linear optimization problem by employing L1norm regularization. A numerical experiment was conducted wherein scenarios of the rate of return of investable assets were generated by using a oneperiod autoregressive model, and the results showed that our investment strategy improves an investment performance more than other strategies from previous studies do.