Conditional tail risk measures for the skewed generalised hyperbolic family

This paper deals with the estimation of loss severity distributions arising from historical data on univariate and multivariate losses. We present an innovative theoretical framework where a closed-form expression for the tail conditional expectation (TCE) is derived for the skewed generalised hyperbolic (GH) family of distributions. The skewed GH family is especially suitable for equity losses because it allows to capture the asymmetry in the distribution of losses that tends to have a heavy right tail. As opposed to the widely used Value-at-Risk, TCE is a coherent risk measure, which takes into account the expected loss in the tail of the distribution. Our theoretical TCE results are verified for different distributions from the skewed GH family including its special cases: Student-t, variance gamma, normal inverse gaussian and hyperbolic distributions. The GH family and its special cases turn out to provide excellent fit to univariate and multivariate data on equity losses. The TCE risk measure computed for the skewed family of GH distributions provides a conservative estimator of risk, addressing the main challenge faced by financial companies on how to reliably quantify the risk arising from the loss distribution. We extend our analysis to the multivariate framework when modelling portfolios of losses, allowing the multivariate GH distribution to capture the combination of correlated risks and demonstrate how the TCE of the portfolio can be decomposed into individual components, representing individual risks in the aggregate (portfolio) loss.     

A hybrid descent method for solving a convex constrained optimization problem with applications

The purpose of this paper is to introduce a hybrid descent algorithm for finding a common point in fixed‐point sets of quasi‐nonexpansive mappings and solution sets of variational inequality problems. In the framework of Hilbert spaces, the strong convergence of the hybrid descent algorithm is established. Numerical experiments for the bandwidth allocation, which demonstrate the effectiveness, performance, and convergence of the proposed algorithm, are provided.     

The maximum surplus in a finite‐time interval for a discrete‐time risk model with exchangeable,dependent claim occurrences

This paper investigates a discrete‐time risk model that involves exchangeable dependent loss generating claim occurrences and compound binomially distributed aggregate loss amounts. First, a general framework is presented to derive the distribution of a surplus sequence using the model. This framework is then applied to obtain the distribution of any function of a surplus sequence in a finite‐time interval. Specifically, the distribution of the maximum surplus is obtained under nonruin conditions. Based on this distribution, the computation of the minimum surplus distribution is given. Asset and risk management–oriented implications are discussed for the obtained distributions based on numerical evaluations. In addition, comparisons are made involving the corresponding results of the classical discrete‐time compound binomial risk model, for which claim occurrences are independent and identically distributed.     

Balanced allocation on graphs: A random walk approach

We propose algorithms for allocating n sequential balls into n bins that are interconnected as a d‐regular n‐vertex graph G, where d ≥ 3 can be any integer. In general, the algorithms proceeds in n succeeding rounds. Let ? > 0 be an integer, which is given as an input to the algorithms. In each round, ball 1 ≤ t ≤ n picks a node of G uniformly at random and performs a nonbacktracking random walk of length ? from the chosen node and simultaneously collects the load information of a subset of the visited nodes. It then allocates itself to one of them with the minimum load (ties are broken uniformly at random). For graphs with sufficiently large girths, we obtain upper and lower bounds for the maximum number of balls at any bin after allocating all n balls in terms of ?, with high probability.     

考虑边流量有限的网络路径博弈问题研究

考虑每条边有流量约束的网络路径博弈问题, 根据收益函数单调递增的特点分析其内在零和性质, 并建模为存在公共边的路径博弈模型。在寻找均衡解的过程中, 首先考虑非合作的情形, 在局中人风险中性的假设下, 给出了求Nash均衡流量分配的标号法并证明该均衡分配的唯一性。接着进一步考虑局中人合作的可能性, 给出模型求得所有局中人的整体最大收益, 并基于纳什谈判模型给出目标函数为凸函数的数学模型确定唯一收益分配方案。事实上, 该方案是对剩余价值的平均分配。最后给出一个算例, 验证本文理论和方法的可行性。关键词:流量约束; 均衡流量; 网络路径博弈; 收益分配     

基于竞合关系的合同制造商融资策略研究

考虑由竞争合同制造商和原始设备生产商(OEM)组成的竞合供应链,竞争合同制造商在上游是OEM的合作者,在下游市场上是OEM的竞争者。当合同制造商因资金约束而不能进行生产运营时,一个通常做法是向银行贷款或者OEM融资;为了更好地探讨竞合供应链的融资决策,考虑了批发价格分别为外生变量和内生变量两种不同的情况下,以OEM为Stackelberg领导者的博弈,这与实际情况很接近。分析结果表明,当批发价格分别为外生变量时,合同制造商融资方式的选择主要受融资利率的影响;当批发价格为内生变量时,合同制造商融资方式的选择主要受自身自有资金量的影响。研究揭示了竞合供应链的融资决策过程,阐明了合同制造商的融资方式选择与自身的自有资金量和融资利率的关系。最后用数值算例对上述结论进行了验证说明。     

考虑联盟结构的联合采购合作剩余分配博弈分析

联合采购合作剩余分配本质是在最大联盟剩余值与最小期望分配值之间的谈判协商过程。当前联合采购合作剩余分配研究主要基于参与企业地位无差别假设,忽略了联盟结构对剩余分配具有明显影响。基于联盟形成的层次结构,研究论证了采购企业通过组建小联盟形式参与更大联盟的联合采购,可提升其在分配谈判中的话语权。通过算例分析表明,考虑联盟结构的联合采购合作剩余分配相对于不考虑联盟结构得到的分配方案更具公平性和合理性。     

碳交易机制下资金约束制造商替代产品的最优生产策略研究

碳交易机制和资金约束在很大程度上影响企业的生产决策,但很少有文献研究碳排放和资金双约束下企业对普通与低碳两种替代品生产决策问题。因此,本文在碳交易机制下讨论了资金约束下制造商两种产品的生产决策问题。本文采用基于有无碳交易和银行融资划分四种情形,基于报童模型构建优化模型分析制造商的最优决策。研究发现:(1)无融资情形下,如果制造商的初始资金很少,则制造商生产更多的普通产品;如果制造商的初始资金很多,则制造商生产更多的低碳产品;(2)在银行融资情形下,当利率较小时,制造商生产更多的低碳产品;当利率较大时,制造商生产更多的普通产品;(3)在银行融资情形下,如果碳排放配额较大,无碳交易机制时的融资量和融资成本高于有碳交易机制时的融资量和融资成本;如果碳排放配额较低则结论相反。     

航空公司中的飞行员配置研究

随着新航线的开辟和新飞机的投入使用,航空公司的任务量急剧增长,飞行员需求的估计和机组的合理配置变得日益重要。本文基于实际工作需求,提出一类用于评估飞行员数量,并进行机组均衡配置的整数规划模型,为航空公司进行飞行员的数量评估和任务分配提供决策支持。本文在以下两个方面做出改进:1)加入国际长途航线,研究国内短途航线和国际长途航线混合搭配情况下飞行员的配置问题;2)鉴于大型整数规划求解的复杂性,通过评估航空公司所需要的飞行员数量的下界,为决策人员制定中长期规划提供依据。本文通过启发式算法进行飞行员的配置,计算结果接近理论问题的下界,证明了算法的有效性。     

Four-dimensional scheduling for uplink dynamic bandwidth allocation in OFDM-PON

Orthogonal frequency division multiplexing passive optical network (OFDM-PON) has been considered a promising access solution to meet the variable bandwidth demand. In this paper, a novel scheduling for dynamic bandwidth allocation (DBA) at medium access control (MAC) layer is proposed for uplink transmission of OFDM-PON. In order to utilize the bandwidth efficiently, scheduling in four dimensions is adopted in the proposed DBA algorithm. Four dimensions stand for frequency domains, time domains, modulation formats and power allocations. The algorithm is quite flexible. Simulation results and analysis show that the proposed algorithm can efficiently utilize the OFDM bandwidth and make the system highly energy-efficient.