Strategy vs risk in margining portfolios of options

The strategy-based approach to portfolio margining has been used for margining customer accounts for more than four decades. The risk-based approach was proposed in the mid eighties for margining some inventory accounts of brokers but permitted for margining customer accounts only in 2005. This paper presents a computational experiment with the strategy-based approach and the risk-based approach with the purpose of clarifying which one yields lower margin requirements under different scenarios. There exists a widespread opinion, cf. (Reuters 2007; Longo 2007; Smith 2008), that the risk-based approach is always a winner in this competition, and therefore the strategy-based approach must be disqualified as outdated. However, the results of our experiment with portfolios of stock options show that, in many practical situations, the strategy-based approach yields substantially lower margin requirements in comparison with the risk-based approach.     

On the Variational Approach to Systems of Quasilinear Conservation Laws

The paper contains results concerning the development of a new approach to the proof of existence theorems for generalized solutions to systems of quasilinear conservation laws. This approach is based on reducing the search for a generalized solution to analyzing extremal properties of a certain set of functionals and is referred to as a variational approach. The definition of a generalized solution can be naturally reformulated in terms of the existence of critical points for a set of functionals, which is convenient within the approach proposed. The variational representation of generalized solutions, which was earlier known for Hopf-type equations, is generalized to systems of quasilinear conservation laws. The extremal properties of the functionals corresponding to systems of conservation laws are described within the variational approach, and a strategy for proving the existence theorem is outlined. In conclusion, it is shown that the variational approach can be generalized to the two-dimensional case.     

Theoretical insights into the augmented-neural-network approach for combinatorial optimization

The augmented-neural-network (AugNN) approach has been applied lately to some NP-Hard combinatorial problems, such as task scheduling, open-shop scheduling and resource-constraint project scheduling. In this approach the problem of search in the solution-space is transformed to a search in a weight-matrix space, much like in a neural-network approach. Some weight adjustment strategies are then used to converge to a good set of weights for a locally optimal solution. While empirical results have demonstrated the effectiveness of the AugNN approach vis-à-vis a few other metaheuristics, little theoretical insights exist which justify this approach and explain the effectiveness thereof. This paper provides some theoretical insights and justification for the AugNN approach through some basic theorems and also describes the algorithm and the formulation with the help of examples.     

Copula方法与相依违约研究

目前信用风险研究的重点已经从单笔债务的违约概率研究转移到多笔债务的相依违约(Dependent Defaults)研究。Copula方法是研究相依违约的重要方法。这种方法是最近几年才被应用到信用领域研究中的一种新方法。本结合代表性献对Copula方法在相依违约研究中的应用进行了探讨。探讨的内容包括Copula方法被应用于相依违约研究的原因、该方法对于相依违约建模理论的改进以及在实证应用中使用Copula方法应该注意的问题。     

On differential equations with interval coefficients

In this study, a new approach is developed to solve the initial value problem for interval linear differential equations. In the considered problem, the coefficients and the initial values are constant intervals. In the developed approach, there is no need to define a derivative for interval-valued functions. All derivatives used in the approach are classical derivatives of real functions. The reason for this is that the solution of the problem is defined as a bunch of real functions. Such a solution concept is compatible also with the robust stability concept. Sufficient conditions are provided for the solution to be expressed analytically. In addition, on a numerical example, the solution obtained by the proposed approach is compared with the solution obtained by the generalized Hukuhara differentiability. It is shown that the proposed approach gives a new type of solution. The main advantage of the proposed approach is that the solution to the considered interval initial value problem exists and is unique, as in the real case.     

A soft approach for hard continuous optimization

This paper is to introduce a soft approach for solving continuous optimizations models where seeking an optimal solution is theoretically or practically impossible.We first review methods for solving continuous optimization models, and argue that only a few optimization models with some good structure are solved. To solve a larger class of optimization problems, we suggest a soft approach by softening the goal in solving a model, and propose a two-stage process for implementing the soft approach. Furthermore, we offer an algorithm for solving optimization models with a convex feasible set, and verify the validity of the soft approach with numerical experiments.     

Portfolio value-at-risk optimization for asymmetrically distributed asset returns

We propose a new approach to portfolio optimization by separating asset return distributions into positive and negative half-spaces. The approach minimizes a newly-defined Partitioned Value-at-Risk (PVaR) risk measure by using half-space statistical information. Using simulated data, the PVaR approach always generates better risk-return tradeoffs in the optimal portfolios when compared to traditional Markowitz mean–variance approach. When using real financial data, our approach also outperforms the Markowitz approach in the risk-return tradeoff. Given that the PVaR measure is also a robust risk measure, our new approach can be very useful for optimal portfolio allocations when asset return distributions are asymmetrical.     

A comparison of analytic and knowledge-based approaches to closed-shop scheduling

This paper compares three different approaches to scheduling in a closed-shop environment, making the case for a knowledge-based approach. A manufacturing example from the food industry is used as a vehicle for the presentation. The first approach attempts to find an optimal solution using a mixed integer linear programming formulation, but the size of the problem renders this approach impractical. The second approach uses a spreadsheet program to obtain feasible solutions, but imbedded assumptions in the heuristics used allow it to be used only for simple demand patterns. The third approach employs expert systems technology. It includes several heuristics and takes all constraints into consideration. The solution obtained may not be optimal, but computational tests suggest that it is far superior to both spreadsheet and manual approaches.     

Finite-Temperature Coarse-Graining of One-Dimensional Models: Mathematical Analysis and Computational Approaches

We present a possible approach for the computation of free energies and ensemble averages of one-dimensional coarse-grained models in materials science. The approach is based upon a thermodynamic limit process, and makes use of ergodic theorems and large deviations theory. In addition to providing a possible efficient computational strategy for ensemble averages, the approach allows for assessing the accuracy of approximations commonly used in practice.     

Supply chain network design: partner selection and production/distribution planning using a systematic model

In this paper, a novel multi-phase mathematical approach is presented for the design of a complex supply chain network. From the point of network design, customer demands, and for maximum overall utility, the important issues are to find suitable and quality companies, and to decide upon an appropriate production/distribution strategy. The proposed approach is based on the genetic algorithm (GA), the analytical hierarchy process (AHP), and the multi-attribute utility theory (MAUT) to satisfy simultaneously the preferences of the suppliers and the customers at each level in the network. A case study with a good quality solution is provided to confirm the efficiency and effectiveness of the proposed approach. Finally, to demonstrate the performance of the proposed approach, a comparative numerical experiment is performed by using the proposed approach and the common single-phase genetic algorithm (SGA). Empirical analysis results demonstrate that the proposed approach can outperform the SGA in partner selection and production/distribution planning for network design.     

Adaptive Rejection Metropolis Simulated Annealing for Detecting Global Maximum Regions

A finite mixture model has been used to fit the data from heterogeneous populations to many applications. An Expectation Maximization (EM) algorithm is the most popular method to estimate parameters in a finite mixture model. A Bayesian approach is another method for fitting a mixture model. However, the EM algorithm often converges to the local maximum regions, and it is sensitive to the choice of starting points. In the Bayesian approach, the Markov Chain Monte Carlo (MCMC) sometimes converges to the local mode and is difficult to move to another mode. Hence, in this paper we propose a new method to improve the limitation of EM algorithm so that the EM can estimate the parameters at the global maximum region and to develop a more effective Bayesian approach so that the MCMC chain moves from one mode to another more easily in the mixture model. Our approach is developed by using both simulated annealing (SA) and adaptive rejection metropolis sampling (ARMS). Although SA is a well-known approach for detecting distinct modes, the limitation of SA is the difficulty in choosing sequences of proper proposal distributions for a target distribution. Since ARMS uses a piecewise linear envelope function for a proposal distribution, we incorporate ARMS into an SA approach so that we can start a more proper proposal distribution and detect separate modes. As a result, we can detect the maximum region and estimate parameters for this global region. We refer to this approach as ARMS annealing. By putting together ARMS annealing with the EM algorithm and with the Bayesian approach, respectively, we have proposed two approaches: an EM-ARMS annealing algorithm and a Bayesian-ARMS annealing approach. We compare our two approaches with traditional EM algorithm alone and Bayesian approach alone using simulation, showing that our two approaches are comparable to each other but perform better than EM algorithm alone and Bayesian approach alone. Our two approaches detect the global maximum region well and estimate the parameters in this region. We demonstrate the advantage of our approaches using an example of the mixture of two Poisson regression models. This mixture model is used to analyze a survey data on the number of charitable donations.     

An integer linear programming approach for a class of bilinear integer programs

We propose an Integer Linear Programming (ILP) approach for solving integer programs with bilinear objectives and linear constraints. Our approach is based on finding upper and lower bounds for the integer ensembles in the bilinear objective function, and using the bounds to obtain a tight ILP reformulation of the original problem, which can then be solved efficiently. Numerical experiments suggest that the proposed approach outperforms a latest iterative ILP approach, with notable reductions in the average solution time.     

An integrated guaranteed- and stochastic-service approach to inventory optimization in supply chains

Multi-echelon inventory optimization literature distinguishes stochastic- (SS) and guaranteed-service (GS) approaches as mutually exclusive frameworks. While the GS approach considers flexibility measures at the stages to deal with stockouts, the SS approach only relies on safety stock. Within a supply chain, flexibility levels might differ between stages rendering them appropriate candidates for one approach or the other. The existing approaches, however, require the selection of a single framework for the entire supply chain instead of a stage-wise choice. We develop an integrated hybrid-service (HS) approach which endogenously determines the overall cost-optimal approach for each stage and computes the required inventory levels. We present a dynamic programming optimization algorithm for serial supply chains that partitions the entire system into subchains of different types. From a numerical study we find that, besides implicitly choosing the better of the two pure frameworks, whose cost differences can be considerable, the HS approach enables additional pipeline and on-hand stock cost savings. We further identify drivers for the preferability of the HS approach.     

The method of approximate particular solutions for solving certain partial differential equations

A standard approach for solving linear partial differential equations is to split the solution into a homogeneous solution and a particular solution. Motivated by the method of fundamental solutions for solving homogeneous equations, we propose a similar approach using the method of approximate particular solutions for solving linear inhomogeneous differential equations without the need of finding the homogeneous solution. This leads to a much simpler numerical scheme with similar accuracy to the traditional approach. To demonstrate the simplicity of the new approach, three numerical examples are given with excellent results. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 506–522, 2012     

The co-production approach to service: a theoretical background

The paper develops a theoretical background on the co-production approach as an extension of operations management principles, in which co-production function assumes well-defined functional form with the input presence of both firm and customers. The co-production approach not only views a customer as a co-producer, but also conducts strategic trade-offs between a firm and customers in service systems. Moreover, the value and the process of value co-creation are also explored under the co-production approach. The experimental study with a hypothetical service system indicates that the co-production function is feasible under economic and institutional considerations, and the co-production approach generalizes both the firm approach and the customer approach. Furthermore, the co-production approach creates many rich opportunities for future research on service operations management.     

Numerical methods for computing sensitivities for ODEs and DDEs

We investigate the performance of the adjoint approach and the variational approach for computing the sensitivities of the least squares objective function commonly used when fitting models to observations. We note that the discrete nature of the objective function makes the cost of the adjoint approach for computing the sensitivities dependent on the number of observations. In the case of ordinary differential equations (ODEs), this dependence is due to having to interrupt the computation at each observation point during numerical solution of the adjoint equations. Each observation introduces a jump discontinuity in the solution of the adjoint differential equations. These discontinuities are propagated in the case of delay differential equations (DDEs), making the performance of the adjoint approach even more sensitive to the number of observations for DDEs. We quantify this cost and suggest ways to make the adjoint approach scale better with the number of observations. In numerical experiments, we compare the adjoint approach with the variational approach for computing the sensitivities.     

Determination of Stackelberg–Nash equilibria using a sensitivity based approach

A sensitivity based approach is presented to determine Nash solution(s) in multiobjective problems modeled as a non-cooperative game. The proposed approach provides an approximation to the rational reaction set (RRS) for each player. An intersection of these sets yields the Nash solution for the game. An alternate approach for generating the RRS based on design of experiments (DOE) combined with response surface methodology (RSM) is also explored. The two approaches for generating the RRS are compared on three example problems to find Nash and Stackelberg solutions. For the examples presented, it is seen that the proposed sensitivity based approach (i) requires less computational effort than a RSM-DOE approach, (ii) is less prone to numerical errors than the RSM-DOE approach, (iii) has the ability to find multiple Nash solutions when the Nash solution is not a singleton, (iv) is able to approximate nonlinear RRS, and (v) on one example problem, found a Nash solution better than the one reported in the literature.     

Exact approaches for testing non-inferiority or superiority of two incidence rates

We studied an unconditional approach based on partial maximization using different penalty values for comparing two incidence rates from Poisson distributions. We also consider a full maximization approach and an approach based on estimation and full maximization. Generally, the third approach has good performance.     

Ant colony optimization and local search for bin packing and cutting stock problems

The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimization problems. Exact solution methods can only be used for very small instances, so for real-world problems, we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In the work presented here, we used an ant colony optimization (ACO) approach to solve both Bin Packing and Cutting Stock Problems. We present a pure ACO approach, as well as an ACO approach augmented with a simple but very effective local search algorithm. It is shown that the pure ACO approach can compete with existing evolutionary methods, whereas the hybrid approach can outperform the best-known hybrid evolutionary solution methods for certain problem classes. The hybrid ACO approach is also shown to require different parameter values from the pure ACO approach and to give a more robust performance across different problems with a single set of parameter values. The local search algorithm is also run with random restarts and shown to perform significantly worse than when combined with ACO.     

A skyline heuristic for the 2D rectangular packing and strip packing problems

In this paper, we propose a greedy heuristic for the 2D rectangular packing problem (2DRP) that represents packings using a skyline; the use of this heuristic in a simple tabu search approach outperforms the best existing approach for the 2DRP on benchmark test cases. We then make use of this 2DRP approach as a subroutine in an “iterative doubling” binary search on the height of the packing to solve the 2D rectangular strip packing problem (2DSP). This approach outperforms all existing approaches on standard benchmark test cases for the 2DSP.