An optimal investment strategy in bank management

This paper considers the application of stochastic optimization theory to asset and capital adequacy management in banking. The Basel II Capital Accord lays down regulations to control bank behaviour, and relies on regulatory ratios such as the capital adequacy ratio (CAR). In an attempt to address the problem of compliance to minimum CAR and under assumptions about retained earnings, loan‐loss reserves, the market and shareholder‐bank owner relationships, we construct a continuous‐time model of the Basel II CAR which is computed from the total risk‐weighted assets (TRWAs) and bank capital in a stochastic setting. In particular, we derive an optimal equity allocation strategy for the bank and monitor the performance of the Basel II CAR under the allocation strategy. Copyright © 2011 John Wiley & Sons, Ltd.     

Finding an efficient solution to linear bilevel programming problem: An effective approach

Multilevel programming is developed to solve the decentralized problem in which decision makers (DMs) are often arranged within a hierarchical administrative structure. The linear bilevel programming (BLP) problem, i.e., a special case of multilevel programming problems with a two level structure, is a set of nested linear optimization problems over polyhedral set of constraints. Two DMs are located at the different hierarchical levels, both controlling one set of decision variables independently, with different and perhaps conflicting objective functions. One of the interesting features of the linear BLP problem is that its solution may not be Paretooptimal. There may exist a feasible solution where one or both levels may increase their objective values without decreasing the objective value of any level. The result from such a system may be economically inadmissible. If the decision makers of the two levels are willing to find an efficient compromise solution, we propose a solution procedure which can generate effcient solutions, without finding the optimal solution in advance. When the near-optimal solution of the BLP problem is used as the reference point for finding the efficient solution, the result can be easily found during the decision process.     

A resource portfolio planning model using sampling-based stochastic programming and genetic algorithm

Resource portfolio planning optimization is crucial to high-tech manufacturing industries. One of the most important characteristics of such a problem is intensive investment and risk in demands. In this study, a nonlinear stochastic optimization model is developed to maximize the expected profit under demand uncertainty. For solution efficiency, a stochastic programming-based genetic algorithm (SPGA) is proposed to determine a profitable capacity planning and task allocation plan. The algorithm improves a conventional two-stage stochastic programming by integrating a genetic algorithm into a stochastic sampling procedure to solve this large-scale nonlinear stochastic optimization on a real-time basis. Finally, the tradeoff between profits and risks is evaluated under different settings of algorithmic and hedging parameters. Experimental results have shown that the proposed algorithm can solve the problem efficiently.     

To split or not to split: Capital allocation with convex risk measures

Convex risk measures were introduced by Deprez and Gerber [Deprez, O., Gerber, H.U., 1985. On convex principles of premium calculation. Insurance: Math. Econom. 4 (3), 179-189]. Here the problem of allocating risk capital to subportfolios is addressed, when convex risk measures are used. The Aumann-Shapley value is proposed as an appropriate allocation mechanism. Distortion-exponential measures are discussed extensively and explicit capital allocation formulas are obtained for the case that the risk measure belongs to this family. Finally the implications of capital allocation with a convex risk measure for the stability of portfolios are discussed. It is demonstrated that using a convex risk measure for capital allocation can produce an incentive for infinite fragmentation of portfolios.     

A Network Optimization Model for Budget Planning in Multi-Objective Hierarchical Systems

This paper presents a planning/budgeting scheme for hierarchical systems. A multi-objective network optimization model for multilayer budget allocation is suggested. The network presents the hierarchical structure of the system. The budget allocations are the flows in the network. Each component in the system (arc in the network) has lower and upper bounds. The model maximizes the additive utility function of the system, expressed as a weighted summation over the preferences of the system's components in the various levels. The preferences are evaluated by using a multigoal approach, utilizing the Analytical Hierarchy Process (AHP). Finally, the model is conceptually compared with other known budgeting procedures and models, such as ZBB, PBBS and cost benefit analyses.     

GlueVaR risk measures in capital allocation applications

GlueVaR risk measures defined by Belles-Sampera et al. (2014) generalize the traditional quantile-based approach to risk measurement, while a subfamily of these risk measures has been shown to satisfy the tail-subadditivity property. In this paper we show how GlueVaR risk measures can be implemented to solve problems of proportional capital allocation. In addition, the classical capital allocation framework suggested by Dhaene et al. (2012) is generalized to allow the application of the Value-at-Risk (VaR) measure in combination with a stand-alone proportional allocation criterion (i.e., to accommodate the Haircut allocation principle). Two new proportional capital allocation principles based on GlueVaR risk measures are defined. An example based on insurance claims data is presented, in which allocation solutions with tail-subadditive risk measures are discussed.     

The hierarchical and social decision making procedure for bi-objective optimization problems by using the simple majority decision rule

Multi-objective optimization has been successfully applied to problems of industrial design, problems of quality control and production management, and problems of finance. The theme of these applications is how to choose the best solution for the decision makers out of a set of non-inferior solutions to a multi-objective optimization problem. For this purpose, an optimization model with hierarchical structure, whose lower problem is a multi-objective optimization problem and the upper problem is a preference optimization problem on a set of non-inferior solutions, must be constructed. This kind of hierarchical problems have been previously analyzed only with regard to linear programming problems by Benson[6]. In this paper, an algorithm is derived that provides a solution as a social choice, obtained by aggregating plural decision-makers' preferences. In the case of the simple majority rule, the bi-objective problem is transformed into an -parameter choice problem, and the golden section method is applied. The availability of the approach is demonstrated with the means of an illustrative example.Technische Universität BerlinFaculty of Science and Technology, Keio University     

Efficient Coordination by Optimal Allocation of Decision Rights for Participants on Electronic Financial Services Markets

Information technology (IT) is enabling large companies and particularly banking firms to create new forms of organizations. Both globalization of markets and stronger regulation throughout the world puts pressure on banking firms to either spend more money coordinating business activities in the traditional hierarchical ways or to employ new forms of organizations enabled by (lower costs of) IT. When facing uncertain demand in multiple horizontal markets, resource allocation problems occur. Accordingly, the location of decision authority in a multilevel hierarchical organization has profound impact on the performance of the firm. The firm has to design its coordination structure, which determines who makes the resource allocation decisions. Considering the tradeoff between pooling effects in the case of centralized decision-making and better assessment of local markets in the case of decentralized decision-making, the decision problem where to locate decision rights to maximize total profits has to be solved. In this paper we investigate for both independent and dependent demands the total profits for each of the possible coordination mechanisms: centralized decision-making, decentralized decision-making, and intermediate-level decision-making. It turns out that—depending on the crucial parameters of the firm—decentralized decision-making or centralized decision-making may be optimal. But in many relevant cases the optimal location of decision rights is at an intermediate level of the hierarchy. We illustrate the findings by considering the banking firm coordinating equity capital allocation by granting alternative decision rights to their employees as participants on electronic financial markets. Finally we discuss the generality of the approach and its applicability in other areas such as inventory management.     

Cooperation in one machine scheduling

A combinatorial optimization problem can often be understood as the problem to minimize cost in a complex situation. If more than one party is involved, the solution of the optimization problem is not the end of the story. In addition it has to be decided how the minimal total cost has to be distributed among the parties involved. In this paper cost allocation problems will be considered arising from one-machine scheduling under additive and weakly increasing cost functions. The approach of the problem will be game theoretical and we shall in fact show that in many cases the games related to the cost allocation problems are balanced.     

Recursive methods for a multi-dimensional risk process with common shocks

In this paper, a multi-dimensional risk model with common shocks is studied. Using a simple probabilistic approach via observing the risk processes at claim instants, recursive integral formulas are developed for the survival probabilities as well as for a class of Gerber-Shiu expected discounted penalty functions that include the surplus levels at ruin. Under the assumption of exponential or mixed Erlang claims, the recursive integrals can be simplified to give recursive sums which are computationally more tractable. Numerical examples including an optimal capital allocation problem are also given towards the end.     

Robust reward–risk ratio optimization with application in allocation of generation asset

In this article, we study reward–risk ratio models under partially known message of random variables, which is called robust (worst-case) performance ratio problem. Based on the positive homogenous and concave/convex measures of reward and risk, respectively, the new robust ratio model is reduced equivalently to convex optimization problems with a min–max optimization framework. Under some specially partial distribution situation, the convex optimization problem is converted into simple framework involving the expectation reward measure and conditional value-at-risk measure. Compared with the existing reward–risk portfolio research, the proposed ratio model has two characteristics. First, the addressed problem combines with two different aspects. One is to consider an incomplete information case in real-life uncertainty. The other is to focus on the performance ratio optimization problem, which can realize the best balance between the reward and risk. Second, the complicated optimization model is transferred into a simple convex optimization problem by the optimal dual theorem. This indeed improves the usability of models. The generation asset allocation in power systems is presented to validate the new models.     

Multi-objective simulation-based evolutionary algorithm for an aircraft spare parts allocation problem

Simulation optimization has received considerable attention from both simulation researchers and practitioners. In this study, we develop a solution framework which integrates multi-objective evolutionary algorithm (MOEA) with multi-objective computing budget allocation (MOCBA) method for the multi-objective simulation optimization problem. We apply it on a multi-objective aircraft spare parts allocation problem to find a set of non-dominated solutions. The problem has three features: huge search space, multi-objective, and high variability. To address these difficulties, the solution framework employs simulation to estimate the performance, MOEA to search for the more promising designs, and MOCBA algorithm to identify the non-dominated designs and efficiently allocate the simulation budget. Some computational experiments are carried out to test the effectiveness and performance of the proposed solution framework.     

考虑外部效应与风险因素的多项目优化模型及应用

多项目的组合优化与资源分配优化,实质上是经济学中资源配置与利用问题.运用经济学与管理学的相关理论和定量研究方法,建立了外部效应估算模型、项目评价模型、风险估算模型、多项目组合优化模型和关于资源分配优化的两层决策模型.相关模型的应用实例研究,说明了该模型的有效性.     

Multi-Path Approach for Reliability-Redundancy Allocation Using a Scaling Method

The reliability-redundancy allocation problem is an optimization problem that achieves better system reliability by determining levels of component redundancies and reliabilities simultaneously. The problem is classified with the hardest problems in the reliability optimization field because the decision variables are mixed-integer and the system reliability function is nonlinear, non-separable, and non-convex. Thus, iterative heuristics are highly recommended for solving the problem due to their reasonable solution quality and relatively short computation time. At present, most iterative heuristics use sensitivity factors to select an appropriate variable which significantly improves the system reliability. The sensitivity factor represents the impact amount of each variable to the system reliability at a designated iteration. However, these heuristics are inefficient in terms of solution quality and computation time because the sensitivity factor calculations are performed only at integer variables. It results in degradation of the exploration and growth in the number of subsequent continuous nonlinear programming (NLP) subproblems. To overcome the drawbacks of existing iterative heuristics, we propose a new scaling method based on the multi-path iterative heuristics introduced by Ha (2004). The scaling method is able to compute sensitivity factors for all decision variables and results in a decreased number of NLP subproblems. In addition, the approximation heuristic for NLP subproblems helps to avoid redundant computation of NLP subproblems caused by outlined solution candidates. Numerical experimental results show that the proposed heuristic is superior to the best existing heuristic in terms of solution quality and computation time.     

On the combinatorial structure of chromatic scheduling polytopes

Chromatic scheduling polytopes arise as solution sets of the bandwidth allocation problem in certain radio access networks, supplying wireless access to voice/data communication networks for customers with individual communication demands. To maintain the links, only frequencies from a certain spectrum can be used, which typically causes capacity problems. Hence it is necessary to reuse frequencies but no interference must be caused by this reuse. This leads to the bandwidth allocation problem, a special case of so-called chromatic scheduling problems. Both problems are NP-hard, and there do not even exist polynomial time algorithms with a fixed quality guarantee.As algorithms based on cutting planes have shown to be successful for many other combinatorial optimization problems, the goal is to apply such methods to the bandwidth allocation problem. For that, knowledge on the associated polytopes is required. The present paper contributes to this issue, exploring the combinatorial structure of chromatic scheduling polytopes for increasing frequency spans. We observe that the polytopes pass through various stages—emptyness, non-emptyness but low-dimensionality, full-dimensionality but combinatorial instability, and combinatorial stability—as the frequency span increases. We discuss the thresholds for this increasing “quantity” giving rise to a new combinatorial “quality” of the polytopes, and we prove bounds on these thresholds. In particular, we prove combinatorial equivalence of chromatic scheduling polytopes for large frequency spans and we establish relations to the linear ordering polytope.     

Pruned Pareto-optimal sets for the system redundancy allocation problem based on multiple prioritized objectives

In this paper, a new methodology is presented to solve different versions of multi-objective system redundancy allocation problems with prioritized objectives. Multi-objective problems are often solved by modifying them into equivalent single objective problems using pre-defined weights or utility functions. Then, a multi-objective problem is solved similar to a single objective problem returning a single solution. These methods can be problematic because assigning appropriate numerical values (i.e., weights) to an objective function can be challenging for many practitioners. On the other hand, methods such as genetic algorithms and tabu search often yield numerous non-dominated Pareto optimal solutions, which makes the selection of one single best solution very difficult. In this research, a tabu search meta-heuristic approach is used to initially find the entire Pareto-optimal front, and then, Monte-Carlo simulation provides a decision maker with a pruned and prioritized set of Pareto-optimal solutions based on user-defined objective function preferences. The purpose of this study is to create a bridge between Pareto optimality and single solution approaches.     

工程建设企业多项目人力资源配置研究——基于胜任力和两阶段优化视角

主要研究工程建设企业多项目人力资源优化配置问题。以项目经理这一关键性人力资源为对象,构建了基于胜任力模型的工程建设企业项目经理能力定级指标体系,给出了具体的能级评价方法,解决了待分配人员的定级和排序问题;在项目优先级和人员能级界定的基础上,以多项目工期均衡和人工总成本最低为目标建立了两阶段优化模型,给出了基于贪婪算法和线性规划的模型求解算法,设计了MATLAB程序对模型进行求解;最后通过实例验证了优化配置模型和求解算法的有效性。     

Dynamic capital allocation with irreversible investments

Capital allocation models generally assume that the risk portfolio is constructed at a single point in time, when the underwriter has full information about available underwriting opportunities. However, in practice, opportunities are not all known at the beginning but instead arrive over time. Moreover, a commitment to an opportunity is not easy to change as time passes. Thus, to optimize a portfolio, the underwriter must make decisions on opportunities as they arrive while making use of assumptions about what will arrive in the future. This paper studies capital allocation rules in this setting, finding important differences from the static setting. The pricing of an opportunity is based on an expected future marginal cost of risk associated with that opportunity—one that will be fully understood only after the risk portfolio is finalized. The risk charge for today’s opportunity is thus a probability-weighted average of the product of the marginal value of capital in future states of the world and the amount of capital consumed by the opportunity in those future states. Our numerical examples illustrate how the marginal cost of risk for an opportunity is shaped by when it arrives in time, as well as what has arrived before it.     

On some multivariate Sarmanov mixed Erlang reinsurance risks: Aggregation and capital allocation

Following some recent works on risk aggregation and capital allocation for mixed Erlang risks joined by Sarmanov’s multivariate distribution, in this paper we present some closed-form formulas for the same topic by considering, however, a different kernel function for Sarmanov’s distribution, not previously studied in this context. The risk aggregation and capital allocation formulas are derived and numerically illustrated in the general framework of stop-loss reinsurance, and then in the particular case with no stop-loss reinsurance. A discussion of the dependency structure of the considered distribution, based on Pearson’s correlation coefficient, is also presented for different kernel functions and illustrated in the bivariate case.     

Relaxation-based algorithms for minimax optimization problems with resource allocation applications

We consider minimax optimization problems where each term in the objective function is a continuous, strictly decreasing function of a single variable and the constraints are linear. We develop relaxation-based algorithms to solve such problems. At each iteration, a relaxed minimax problem is solved, providing either an optimal solution or a better lower bound. We develop a general methodology for such relaxation schemes for the minimax optimization problem. The feasibility tests and formulation of subsequent relaxed problems can be done by using Phase I of the Simplex method and the Farkas multipliers provided by the final Simplex tableau when the corresponding problem is infeasible. Such relaxation-based algorithms are particularly attractive when the minimax optimization problem exhibits additional structure. We explore special structures for which the relaxed problem is formulated as a minimax problem with knapsack type constraints; efficient algorithms exist to solve such problems. The relaxation schemes are also adapted to solve certain resource allocation problems with substitutable resources. There, instead of Phase I of the Simplex method, a max-flow algorithm is used to test feasibility and formulate new relaxed problems.Corresponding author.Work was partially done while visiting AT&T Bell Laboratories.