Roy H. Kwon

Robust portfolio selection for index tracking

Abstract We develop a robust portfolio selection model for tracking a market index using a subset of its assets. The model is a 0–1 integer program that seeks to maximize similarity between selected assets and the assets of the target index. We allow uncertainty in the objective function by using a computationally tractable robust framework that can control the conservativeness of the solution. This protects against worst-case realizations of potential estimation errors and other deviations. Out-of-sample experiments using the S&P 100 demonstrate the advantages of the robust model. Compared to portfolios constructed with the nominal model, moderately conservative robust portfolios are shown to have lower tracking error and risk profiles that are more similar to the target index.

Iterative Combinatorial Auctions with Bidder-Determined Combinations

In combinatorial auctions, multiple distinct items are sold simultaneously and a bidder may place a single bid on a set (package) of distinct items. The determination of packages for bidding is a nontrivial task, and existing efficient formats require that bidders know the set of packages and/or their valuations. In this paper, we extend an efficient ascending combinatorial auction mechanism to use approximate single-item pricing. The single-item prices in each round are derived from a linear program that is constructed to reflect the current allocation of packages. Introduction of approximate single-item prices allows for endogenous bid determination where bidders can discover packages that were not included in the original bid set. Due to nonconvexities, single-item prices may not exist that are exact marginal values. We show that the use of approximate single-item prices with endogenous bidding always produces allocations that are at least as efficient as those from bidding with a fixed set of packages based on package pricing. A network resource allocation example is given that illustrates the benefits of our endogenous bidding mechanism.

Optimization-Based Bidding in Day-Ahead Electricity Auction Markets: A Review of Models for Power Producers

We review some mathematical programming models that capture the optimal bidding problem that power producers face in day-ahead electricity auction markets. The models consider both price-taking and non-price taking assumptions. The models include linear and non-linear integer programming models, mathematical programs with equilibrium constraints, and stochastic programming models with recourse. Models are emphasized where the producer must self-schedule units and therefore must integrate optimal bidding with unit commitment decisions. We classify models according to whether competition from competing producers is directly incorporated in the model.

Optimizing the Deployment of Public Access Defibrillators

Out-of-hospital cardiac arrest is a significant public health issue, and treatment, namely, cardiopulmonary resuscitation and defibrillation, is very time sensitive. Public access defibrillation programs, which deploy automated external defibrillators (AEDs) for bystander use in an emergency, reduce the time to defibrillation and improve survival rates. In this paper, we develop models to guide the deployment of public AEDs. Our models generalize existing location models and incorporate differences in bystander behavior. We formulate three mixed integer nonlinear models and derive equivalent integer linear reformulations or easily computable bounds. We use kernel density estimation to derive a spatial probability distribution of cardiac arrests that is used for optimization and model evaluation. Using data from Toronto, Canada, we show that optimizing AED deployment outperforms the existing approach by 40% in coverage, and substantial gains can be achieved through relocating existing AEDs. Our results suggest that improvements in survival and cost-effectiveness are possible with optimization.

A Stochastic-Goal Mixed-Integer Programming approach for integrated stock and bond portfolio optimization

We consider a Stochastic-Goal Mixed-Integer Programming (SGMIP) approach for an integrated stock and bond portfolio problem. The portfolio model integrates uncertainty in asset prices as well as several important real-world trading constraints. The resulting formulation is a structured large-scale problem that is solved using a model specific algorithm that consists of a decomposition, warm-start, and iterative procedure to minimize constraint violations. We present computational results and portfolio return values in comparison to a market performance measure. For many of the test cases the algorithm produces optimal solutions, where CPU time is improved greatly.

Modeling and optimization of the electromechanical behavior of an ionic polymer–metal composite

The electroactive behavior of an ionic polymer–metal composite (IPMC) actuator was modeled and the optimum design parameters for actuation were also studied. An actuation model characterizing the mechanical response of the IPMC under a given electrical field was proposed considering the electro-chemical parameters. To find the optimum conditions maximizing the tip deflection and blocking force, a multivariable constrained optimization equation was proposed in which the saturation level of hydration, applied voltage and the thickness of IPMC were used as decision variables. IPMC samples with variable thickness were manufactured based on a Nafion membrane and the effect of decision variables on the tip deflection, blocking force and response time of the IPMC was studied. The proposed model and the simulation of optimization were validated by experiment.

Data dependent worst case bounds for weighted set packing

We develop data dependent worst case bounds for three simple greedy algorithms for the maximum weighted independent set problem applied to maximum weighted set packing. We exploit the property that the generated output will attain at least a certain weight. These weight quantities are a function of the individual weights corresponding to the vertices of the problem. By using an argument based on linear programming duality we develop a priori bounds that are a function of the minimum guaranteed weight quantities, the highest average reward for a ground item, and cardinality of the ground set. This extends the current bounds which are only a function of the maximum vertex degree in the associated conflict graph. Examples are given that show the benefits of incorporating this data dependent information into bounds.

Portfolio selection under model uncertainty: a penalized moment-based optimization approach

We present a new approach that enables investors to seek a reasonably robust policy for portfolio selection in the presence of rare but high-impact realization of moment uncertainty. In practice, portfolio managers face difficulty in seeking a balance between relying on their knowledge of a reference financial model and taking into account possible ambiguity of the model. Based on the concept of Distributionally Robust Optimization (DRO), we introduce a new penalty framework that provides investors flexibility to define prior reference models using the distributional information of the first two moments and accounts for model ambiguity in terms of extreme moment uncertainty. We show that in our approach a globally-optimal portfolio can in general be obtained in a computationally tractable manner. We also show that for a wide range of specifications our proposed model can be recast as semidefinite programs. Computational experiments show that our penalized moment-based approach outperforms classical DRO approaches in terms of both average and downside-risk performance using historical data.

Fabrication, modeling and optimization of an ionic polymer gel actuator

The modeling of the electro-active behavior of ionic polymer gel is studied and the optimum conditions that maximize the deflection of the gel are investigated. The bending deformation of polymer gel under an electric field is formulated by using chemo-electro-mechanical parameters. In the modeling, swelling and shrinking phenomena due to the differences in ion concentration at the boundary between the gel and solution are considered prior to the application of an electric field, and then bending actuation is applied. As the driving force of swelling, shrinking and bending deformation, differential osmotic pressure at the boundary of the gel and solution is considered. From this behavior, the strain or deflection of the gel is calculated. To find the optimum design parameter settings (electric voltage, thickness of gel, concentration of polyion in the gel, ion concentration in the solution, and degree of cross-linking in the gel) for bending deformation, a nonlinear constrained optimization model is formulated. In the optimization model, a bending deflection equation of the gel is used as an objective function, and a range of decision variables and their relationships are used as constraint equations. Also, actuation experiments are conducted using poly(2-acrylamido-2-methylpropane sulfonic acid) (PAMPS) gel and the optimum conditions predicted by the proposed model have been verified by the experiments.

Semidefinite Programming Approaches for Bounding Asian Option Prices

Semidefinite programming (SDP) approaches are considered for obtaining bounds for the price of an arithmetic average Asian option. A method for computing the moments of the distribution of prices is developed which enables the method of Bertsimas and Popescu to be extended for the case of the Asian option. In particular, several SDP formulations for upper and lower bounds of the price of an Asian option are given based on different representations of the payoffs of the option. The formulations are amenable to standard SDP computational methods.