A multicast problem with shared risk cost

In this paper, we study a minimum cost multicast problem on a network with shared risk link groups (SRLGs). Each SRLG contains a set of arcs with a common risk, and there is a cost associated with it. The objective of the problem is to find a multicast tree from the source to a set of destinations with minimum transmission cost and risk cost. We present a basic model for the multicast problem with shared risk cost (MCSR) based on the well-known multicommodity flow formulation for the Steiner tree problem (Goemans and Myung in Networks 1:19–28, 1993; Polzin and Daneshmand in Discrete Applied Mathematics 112(1–3): 241–261, 2001). We propose a set of strong valid inequalities to tighten the linear relaxation of the basic model. We also present a mathematical model for undirected MCSR. The computational results of real life test instances demonstrate that the new valid inequalities significantly improve the linear relaxation bounds of the basic model, and reduce the total computation time by half in average.     

Assessing the cost of capital for longevity risk

The cost of capital is a key element of the embedded value methodology for the valuation of a life business. Further, under some solvency approaches (in particular, the Swiss Solvency Test and the developing Solvency 2 project) assessing the cost of capital constitutes a step in determining the required capital allocation.Whilst the cost of capital is usually meant as a reward for the risks encumbering a given life portfolio, in actuarial practice the relevant parameter has been traditionally chosen, at least to some extent, inconsistently with such risks. The adoption of market-consistent valuations has then been advocated to reach a common standard.A market-consistent value usually acknowledges a reward to shareholders’ capital as long as the market does, namely if the risk is systematic or undiversifiable. When dealing with a life annuity portfolio (or a pension plan), an important example of systematic risk is provided by the longevity risk, i.e. the risk of systematic deviations from the forecasted mortality trend. Hence, a market-consistent approach should provide appropriate valuation tools.In this paper we refer to a portfolio of immediate life annuities and we focus on longevity risk. Our purpose is to design a framework for a valuation of the portfolio which is market-consistent, and therefore based on a risk-neutral argument, while involving some of the basic items of a traditional valuation, viz best estimate future flows and allocated capital. This way, we try to reconcile the traditional with a market-consistent (or risk-neutral) approach. This allows us, in particular, to translate the results obtained under the risk-neutral approach in terms of a properly redefined embedded value.     

A DEA analysis of risk,cost, and revenues in insurance

Insurance companies have to take risk and cost into account when pricing car insurance policies that cover the risk of private use of cars. In this paper we use data from 80?000 car insurance policies in order to assess, once risk and cost have been taken into account, the combinations of risk that generate the highest returns for the company under existing pricing practices. We use data envelopment analysis (DEA) and frame the study within an analysis of experiments context. The results of DEA are interpreted in a multivariate statistical analysis context using factor analysis, and property fitting techniques. The impact of risk factors in the efficiency is explored by means of regression analysis with dummy variables. There are consequences for the pricing policy of the company.     

基于非参数分布的沪深股市VaR测度

沪深大盘指数的收益率分布函数并不服从通常人们所认为的正态分布.因此,采用一种新的方法—非参数核密度估计,对沪深股指收益率分布进行拟合.该方法不仅很好地刻画了收益率分布的尖峰和肥尾特征,而且由此建立的VaR模型比一般的基于参数分布的VaR模型更能捕捉市场的风险特征,结论也更加准确.     

带基差风险和交易费用的不完全市场下的期权定价方法

本文研究了同时带有基差风险和交易费用的不安全市场中的权证定价方法。把[1]的模型推广到了考虑基差风险的情况[2]。期权的价格以一个三维自由边界问题的解给出,并含有两个相关的股票价格变量的相关系数。     

Mathematical programming approaches for dual multicast routing problem with multilayer risk cost

This paper addresses a dual multicast routing problem with shared risk link group (SRLG) diverse costs (DMR-SRLGD) that arises from large-scale distribution of realtime multicast data (e.g., internet protocol TV, videocasting, online games, stock price update). The goal of this problem is to find two redundant multicast trees, each from one of the two sources to every destination at a minimum cost. The cost of the problem contains two parts: the multicast routing cost and the shard common risk cost. Such common risk could cause the failures of multiple links simultaneously. Therefore, the DMR-SRLGD ensures the availability and reliability of multicast service. We formulate an edge-based model for the DMR-SRLGD. In addition, we also propose a path-based model that rises from the Dantzig-Wolfe decomposition of the edge-based model, and develop a column-generation framework to solve the linear relaxation of the path-based formulation. We then employ a branch-and-price solution method to find integer solutions to DMR-SRLGD. We also extend both edge-based and path-based models to handle the complex quality of service requirements. The computational results show the edge-based model is superior than the path-based model for the easy and small test instances, whereas the path-based model provides better solutions in a timely fashion for hard or large test instances.     

Optimal spot market inventory strategies in the presence of cost and price risk

We consider a firm facing random demand at the end of a single period of random length. At any time during the period, the firm can either increase or decrease inventory by buying or selling on a spot market where price fluctuates randomly over time. The firm’s goal is to maximize expected discounted profit over the period, where profit consists of the revenue from selling goods to meet demand, on the spot market, or in salvage, minus the cost of buying goods, and transaction, penalty, and holding costs. We first show that this optimization problem is equivalent to a two-dimensional singular control problem. We then use a recently developed control-theoretic approach to show that the optimal policy is completely characterized by a simple price-dependent two-threshold policy. In a series of computational experiments, we explore the value of actively managing inventory during the period rather than making a purchase decision at the start of the period, and then passively waiting for demand. In these experiments, we observe that as price volatility increases, the value of actively managing inventory increases until some limit is reached.     

Longevity risk,cost of capital and hedging for life insurers under Solvency II

The cost of capital is an important factor determining the premiums charged by life insurers issuing life annuities. This capital cost can be reduced by hedging longevity risk with longevity swaps, a form of reinsurance. We assess the costs of longevity risk management using indemnity based longevity swaps compared to costs of holding capital under Solvency II. We show that, using a reasonable market price of longevity risk, the market cost of hedging longevity risk for earlier ages is lower than the cost of capital required under Solvency II. Longevity swaps covering higher ages, around 90 and above, have higher market hedging costs than the saving in the cost of regulatory capital. The Solvency II capital regulations for longevity risk generates an incentive for life insurers to hold longevity tail risk on their own balance sheets, rather than transferring this to the reinsurance or the capital markets. This aspect of the Solvency II capital requirements is not well understood and raises important policy issues for the management of longevity risk.     

Supply chain network operations management of a blood banking system with cost and risk minimization

Blood service operations are a key component of the healthcare system all over the world and yet the modeling and the analysis of such systems from a complete supply chain network optimization perspective have been lacking due to their associated unique challenges. In this paper, we develop a generalized network optimization model for the complex supply chain of human blood, which is a life-saving, perishable product. In particular, we consider a regionalized blood banking system consisting of collection sites, testing and processing facilities, storage facilities, distribution centers, as well as points of demand, which, typically, include hospitals. Our multicriteria system-optimization approach on generalized networks with arc multipliers captures many of the critical issues associated with blood supply chains such as the determination of the optimal allocations, and the induced supply-side risk, as well as the induced cost of discarding the waste, while satisfying the uncertain demands as closely as possible. The framework that we present is also applicable, with appropriate modifications, to the optimization of other supply chains of perishable products.     

Marginal cost price rule for homogeneous cost functions

Mirman and Tauman (1982) show that axioms of cost sharing, additivity, rescaling invariance, monotonicity, and consistency uniquely determine a price rule on the class of continuously differentiable cost problems as the Aumann-Shapley price mechanism. Here we prove that standard versions of these axioms determine uniquely the marginal cost price rule on the class of homogeneous and convex cost functions, which are, in addition, continuously differentiable. This result persists even if the cost functons are not required to be convex. Received: August 2001     

Optimizing cost flows by edge cost and capacity upgrade

We examine a network upgrade problem for cost flows. A budget can be distributed among the arcs of the network. An investment on each single arc can be used either to decrease the arc flow cost, or to increase the arc capacity, or both. The goal is to maximize the flow through the network while not exceeding bounds on the budget and on the total flow cost.

The problems are NP-hard even on series-parallel graphs. We provide an approximation algorithm on series-parallel graphs which, for arbitrary δ,>0, produces a solution which exceeds the bounds on the budget and the flow cost by factors of at most 1+δ and 1+, respectively, while the amount of flow is at least that of an optimum solution. The running time of the algorithm is polynomial in the input size and 1/(δ). In addition we give an approximation algorithm on general graphs applicable to problem instances with small arc capacities.     

Managing contribution and capital market risk in a funded public defined benefit plan: Impact of CVaR cost constraints

Using a Monte Carlo framework, we analyze the risks and rewards of moving from an unfunded defined benefit pension system to a funded plan for German civil servants, allowing for alternative strategic contribution and investment patterns. In the process we integrate a Conditional Value at Risk (CVaR) restriction on overall plan costs into the pension manager’s objective of controlling contribution rate volatility. After estimating the contribution rate that would fully fund future benefit promises for current and prospective employees, we identify the optimal contribution and investment strategy that minimizes contribution rate volatility while restricting worst-case plan costs. Finally, we analyze the time path of expected and worst-case contribution rates to assess the chances of reduced contribution rates for current and future generations. Our results show that moving toward a funded public pension system can be beneficial for both civil servants and taxpayers.     

Consistent cost sharing

A new concept of consistency for cost sharing solutions is discussed, analyzed, and related to the homonymous and natural property within the rationing context. Main result is that the isomorphism in Moulin and Shenker (J Econ Theory 64:178–201, 1994) pairs each additive and consistent single-valued mechanism with a corresponding monotonic and consistent rationing method. Then this answers the open question in Moulin (Econometrica 68:643–684, 2000; Handbook of social choice and welfare. Handbooks in economics, pp 289–357, 2002) whether such notion for cost sharing exists. The conclusion is that renown solutions like the average and serial cost sharing mechanisms are consistent, whereas the Shapley–Shubik mechanism is not. Average cost sharing is the only strongly consistent element in this class. The two subclasses of incremental and parametric cost sharing mechanisms are further analyzed as refinement of the main result.     

Allocative cost of weighted discrimination

Discrimination, whether of the reverse of the usual kind, distorts the allocation of resources in favour of, respectively against, the group or individual concerned. Affirmative action and institutional distinction extraneous to work performance are examples where more weight is attached to the agent's subsequent output than is warranted by its intrinsic merit. We introduce this extra weight as a discrimination factor and propose a method of measuring the allocative effect on resources. Inasmuch as the discrimination factor measures a bias in the agent's behavior setting the article is relevant to eco-behavioral research.     

Balancedness of infrastructure cost games

In this paper we study the class of infrastructure cost games. A game in this class models the infrastructure costs (both building and maintenance) produced when a set of users of different types makes use of a certain infrastructure, which may consist of several facilities. Special attention is paid to one facility infrastructure cost games. Such games are modeled as the sum of an airport game and a maintenance cost game. It turns out that the core and nucleolus of these games are very closely related to the core and nucleolus of an associated generalized airport game. Furthermore we provide necessary and sufficient conditions under which an infrastructure cost game is balanced.