Particle swarm optimization approach to portfolio optimization

The survey of the relevant literature showed that there have been many studies for portfolio optimization problem and that the number of studies which have investigated the optimum portfolio using heuristic techniques is quite high. But almost none of these studies deals with particle swarm optimization (PSO) approach. This study presents a heuristic approach to portfolio optimization problem using PSO technique. The test data set is the weekly prices from March 1992 to September 1997 from the following indices: Hang Seng in Hong Kong, DAX 100 in Germany, FTSE 100 in UK, S&P 100 in USA and Nikkei in Japan. This study uses the cardinality constrained mean-variance model. Thus, the portfolio optimization model is a mixed quadratic and integer programming problem for which efficient algorithms do not exist. The results of this study are compared with those of the genetic algorithms, simulated annealing and tabu search approaches. The purpose of this paper is to apply PSO technique to the portfolio optimization problem. The results show that particle swarm optimization approach is successful in portfolio optimization.     

On generalized semi-infinite optimization and bilevel optimization

The paper studies the connections and differences between bilevel problems (BL) and generalized semi-infinite problems (GSIP). Under natural assumptions (GSIP) can be seen as a special case of a (BL). We consider the so-called reduction approach for (BL) and (GSIP) leading to optimality conditions and Newton-type methods for solving the problems. We show by a structural analysis that for (GSIP)-problems the regularity assumptions for the reduction approach can be expected to hold generically at a solution but for general (BL)-problems not. The genericity behavior of (BL) and (GSIP) is in particular studied for linear problems.     

A gap between multiobjective optimization and scalar optimization

We give an example to illustrate a gap between multiobjective optimization and single-objective optimization, which solves a problem proposed in Ref. 1.     

真实利率波动对长期资产配置的影响(英)

对于单期的投资者而言,无违约风险的固定收益证券被视为无风险资产.这是因为固定收益证券的收益率在投资的初期就能确定.然而在考虑长期的投资时,投资者可以调整资产配置,固定收益证券也将面临再投资的利率波动风险,因此不能再被视为无风险资产.本文在一类特殊的``习惯形成"效用函数的框架下讨论长期资产配置.在一系列为简化问题而作的假设之下,本文推导出了真实利率波动对风险资产配置权重的影响,并且为计算实际长期资产配置的最优比例提供了理论依据和算法.     

Discrete optimization

A survey of some theoretical concepts in discrete optimization is given.     

Interactive optimization

Optimization algorithms or heuristics in which the user interacts significantly either during the solution process or as part of post-optimality analysis are becoming increasingly popular. An important underlying premise of such man/ machine systems is that there are some steps in solving a problem in which the computer has an advantage and other steps in which a human has an advantage. This paper first discusses how man/machine systems can be useful in facilitating model specification and revision, coping with aspects of a problem that are difficult to quantify and assisting in the solution process. We then survey successful systems that have been developed in the areas of vehicle scheduling, location problems, job shop scheduling, course scheduling, and planning language-based optimization.     

Interactive optimization

Optimization algorithms or heuristics in which the user interacts significantly either during the solution process or as part of post-optimality analysis are becoming increasingly popular. An important underlying premise of such man/machine systems is that there are some steps in solving a problem in which the computer has an advantage and other steps in which a human has an advantage. This paper first discusses how man/machine systems can be useful in facilitating model specification and revision, coping with aspects of a problem that are difficult to quantify and assisting in the solution process. We then survey successful systems that have been developed in the areas of vehicle scheduling, location problems, job shop scheduling, course scheduling, and planning language-based optimization.     

Scenario optimization

Uncertainty in the parameters of a mathematical program may present a modeller with considerable difficulties. Most approaches in the stochastic programming literature place an apparent heavy data and computational burden on the user and as such are often intractable. Moreover, the models themselves are difficult to understand. This probably explains why one seldom sees a fundamentally stochastic model being solved using stochastic programming techniques. Instead, it is common practice to solve a deterministic model with different assumed scenarios for the random coefficients. In this paper we present a simple approach to solving a stochastic model, based on a particular method for combining such scenario solutions into a single, feasible policy. The approach is computationally simple and easy to understand. Because of its generality, it can handle multiple competing objectives, complex stochastic constraints and may be applied in contexts other than optimization. To illustrate our model, we consider two distinct, important applications: the optimal management of a hydro-thermal generating system and an application taken from portfolio optimization.     

A hybrid stochastic optimization framework for composite nonconvex optimization

Mathematical Programming - We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea...     

Robust multiobjective optimization & applications in portfolio optimization

Motivated by Markowitz portfolio optimization problems under uncertainty in the problem data, we consider general convex parametric multiobjective optimization problems under data uncertainty. For the first time, this uncertainty is treated by a robust multiobjective formulation in the gist of Ben-Tal and Nemirovski. For this novel formulation, we investigate its relationship to the original multiobjective formulation as well as to its scalarizations. Further, we provide a characterization of the location of the robust Pareto frontier with respect to the corresponding original Pareto frontier and show that standard techniques from multiobjective optimization can be employed to characterize this robust efficient frontier. We illustrate our results based on a standard mean–variance problem.     

Multiobjective optimization using differential evolution for real-world portfolio optimization

Portfolio optimization is an important aspect of decision-support in investment management. Realistic portfolio optimization, in contrast to simplistic mean-variance optimization, is a challenging problem, because it requires to determine a set of optimal solutions with respect to multiple objectives, where the objective functions are often multimodal and non-smooth. Moreover, the objectives are subject to various constraints of which many are typically non-linear and discontinuous. Conventional optimization methods, such as quadratic programming, cannot cope with these realistic problem properties. A valuable alternative are stochastic search heuristics, such as simulated annealing or evolutionary algorithms. We propose a new multiobjective evolutionary algorithm for portfolio optimization, which we call DEMPO??Differential Evolution for Multiobjective Portfolio Optimization. In our experimentation, we compare DEMPO with quadratic programming and another well-known evolutionary algorithm for multiobjective optimization called NSGA-II. The main advantage of DEMPO is its ability to tackle a portfolio optimization task without simplifications, while obtaining very satisfying results in reasonable runtime.     

Two-stage based ensemble optimization framework for large-scale global optimization

Large-scale global optimization (LSGO) is a very important and challenging task in optimization domain, which is embedded in many scientific and engineering applications. In order to strengthen both effectiveness and efficiency of LSGO algorithm, this paper designs a two-stage based ensemble optimization evolutionary algorithm (EOEA) framework, which serially implements two sub-optimizers. These two sub-optimizers mainly focus on exploration and exploitation separately. The EOEA framework can be easily generated, flexibly altered and modified, according to different implementation conditions. In order to analyze the effects of EOEA’s components, we compare its performance on diverse kinds of problems with its two sub-optimizers and three variants. To show its superiorities over the previous LSGO algorithms, we compare its performance with six classical LSGO algorithms on the LSGO test functions of IEEE Congress of Evolutionary Computation (CEC 2008). The performance of EOEA is further evaluated by experimental comparison with four state-of-the-art LSGO algorithms on the test functions of CEC 2010 LSGO competition. To benchmark the practical applicability of EOEA, we adopt EOEA to the parameter calibration problem of water pipeline system. Based on the experimental results on diverse scales of systems, EOEA performs steadily and robustly.     

鲁棒信用风险优化的线性锥优化模型

考虑了具有强健性的信用风险优化问题. 根据最差条件在值风险度量信用风险的方法,建立了信用风险优化问题的模型. 由于信用风险的损失分布存在不确定性,考虑了两类不确定性区间,即箱子型区间和椭球型区间. 把具有强健性的信用风险优化问题分别转化成线性规划问题和二阶锥规划问题. 最后,通过一个信用风险问题的例子来说明此模型的有效性.     

Portfolio optimization by minimizing conditional value-at-risk via nondifferentiable optimization

Conditional Value-at-Risk (CVaR) is a portfolio evaluation function having appealing features such as sub-additivity and convexity. Although the CVaR function is nondifferentiable, scenario-based CVaR minimization problems can be reformulated as linear programs (LPs) that afford solutions via widely-used commercial softwares. However, finding solutions through LP formulations for problems having many financial instruments and a large number of price scenarios can be time-consuming as the dimension of the problem greatly increases. In this paper, we propose a two-phase approach that is suitable for solving CVaR minimization problems having a large number of price scenarios. In the first phase, conventional differentiable optimization techniques are used while circumventing nondifferentiable points, and in the second phase, we employ a theoretically convergent, variable target value nondifferentiable optimization technique. The resultant two-phase procedure guarantees infinite convergence to optimality. As an optional third phase, we additionally perform a switchover to a simplex solver starting with a crash basis obtained from the second phase when finite convergence to an exact optimum is desired. This three phase procedure substantially reduces the effort required in comparison with the direct use of a commercial stand-alone simplex solver (CPLEX 9.0). Moreover, the two-phase method provides highly-accurate near-optimal solutions with a significantly improved performance over the interior point barrier implementation of CPLEX 9.0 as well, especially when the number of scenarios is large. We also provide some benchmarking results on using an alternative popular proximal bundle nondifferentiable optimization technique.     

Robust optimization approximation for joint chance constrained optimization problem

Chance constraint is widely used for modeling solution reliability in optimization problems with uncertainty. Due to the difficulties in checking the feasibility of the probabilistic constraint and the non-convexity of the feasible region, chance constrained problems are generally solved through approximations. Joint chance constrained problem enforces that several constraints are satisfied simultaneously and it is more complicated than individual chance constrained problem. This work investigates the tractable robust optimization approximation framework for solving the joint chance constrained problem. Various robust counterpart optimization formulations are derived based on different types of uncertainty set. To improve the quality of robust optimization approximation, a two-layer algorithm is proposed. The inner layer optimizes over the size of the uncertainty set, and the outer layer optimizes over the parameter t which is used for the indicator function upper bounding. Numerical studies demonstrate that the proposed method can lead to solutions close to the true solution of a joint chance constrained problem.