Convex risk measures for the aggregation of multiple information sources and applications in insurance

We propose a novel class of convex risk measures, based on the concept of the Fréchet mean, designed in order to handle uncertainty which arises from multiple information sources regarding the risk factors of interest. The proposed risk measures robustly characterize the exposure of the firm, by filtering out appropriately the partial information available in individual sources into an aggregate model for the risk factors of interest. Importantly, the proposed risks can be expressed in closed analytic forms allowing for interesting qualitative interpretations as well as comparative statics and thus facilitate their use in the everyday risk management process of the insurance firms. The potential use of the proposed risk measures in insurance is illustrated by two concrete applications, capital risk allocation and premia calculation under uncertainty.     

无穷范数松弛的低复杂度超奈奎斯特检测

超奈奎斯特(Faster-than-Nyquist,FTN)速率传输可以有效提高频谱效率，但这种非正交传输方式引入的严重码间串扰相应提高了接收端的处理难度。针对该问题，设计了一种基于循环成块传输的低复杂度检测算法。最优检测被建模为无约束的二元二次规划(Boolean Quadratic Program,BQP)问题，为了求解该NP-hard问题，采用无穷范数约束松弛原问题的非凸可行解集，并基于次梯度下降法提出松弛问题的有效优化算法。数值仿真结果表明，所提算法在误比特率(Bit Error Rate,BER)性能上优于频域均衡，且在可接受的性能损失范围内算法执行效率远高于理论最优的最大似然序列估计(Maximum Likelihood Sequence Estimation,MLSE)。     

Hypercongestion in production correspondences: an empirical exploration

This empirical contribution reviews the rather limited existing literature measuring congestion in production. It first compares current ways to measure congestion using nonparametric specifications of technologies. In particular, it focuses on the magnitude and incidence of the congestion detected in empirical studies using traditional radial efficiency measures. Thereafter, it shows the limitations of this radial measurement and how alternative measurement schemes may reveal higher amounts of congestion. Then, the new, more general methodology of measuring S-congestion is presented. In particular, we first present a numerical example to illustrate the way the S-disposable technologies allow to capture more extreme forms of congestion by setting empirically determined upper bounds to the wasting of inputs. Then, an empirical illustration is presented based on an existing sample of data. A final section concludes.     

Tail mutual exclusivity and Tail-VaR lower bounds

In this paper, we extend the concept of mutual exclusivity proposed by [Dhaene, J. & Denuit, M. (1999). The safest dependence structure among risks. Insurance: Mathematics and Economics 25, 11–21] to its tail counterpart and baptize this new dependency structure as tail mutual exclusivity. Probability levels are first specified for each component of the random vector. Under this dependency structure, at most one exceedance over the corresponding Value-at-Risks (VaRs) is possible, the other components being zero in such a case. No condition is imposed when all components stay below the VaRs. Several properties of this new negative dependence concept are derived. We show that this dependence structure gives rise to the smallest value of Tail-VaR (TVaR) of a sum of risks within a given Fréchet space, provided that the probability level of the TVaR is close enough to one.     

A Brief Survey of Modern Optimization for Statisticians

Modern computational statistics is turning more and more to high‐dimensional optimization to handle the deluge of big data. Once a model is formulated, its parameters can be estimated by optimization. Because model parsimony is important, models routinely include non‐differentiable penalty terms such as the lasso. This sober reality complicates minimization and maximization. Our broad survey stresses a few important principles in algorithm design. Rather than view these principles in isolation, it is more productive to mix and match them. A few well‐chosen examples illustrate this point. Algorithm derivation is also emphasized, and theory is downplayed, particularly the abstractions of the convex calculus. Thus, our survey should be useful and accessible to a broad audience.     

采用目标假设的三被动式传感器数据关联算法

被动式传感器目标跟踪是多传感器多目标跟踪领域的一个重要研究方向。针对三被动式传感器多目标定位系统全局最优数据关联的三维分配问题，在允许传感器漏检和虚警的情况下，通过分析拉格朗日松弛算法，提出一种假定真实目标的快速收敛算法。该算法通过粗关联假定真实目标并重新修改代价矩阵，然后进行细关联，使得拉格朗日松弛算法在保证关联精度的前提下有效地提高了收敛速度。理论分析和实验结果表明，该算法提高了数据关联的速度,并在一定程度上提高了关联准确率。     

Profitability efficiency,marketability efficiency and technology gaps in Taiwan’s banking industry: meta-frontier network data envelopment analysis

The aim of this article is to measure the profitability efficiency (PE) and marketability efficiency (ME) of non-homogenous Taiwanese banks after the adoption of International Financial Reporting Standards by using the convex meta-frontier data envelopment analysis model. The model is applied to simultaneously estimate PE and ME of the banks in financial holding companies (FHCs) and the banks not in FHCs. The meta-inefficiencies in individual processes are further decomposed into group inefficiencies and technology gap inefficiencies to explore the sources of inefficiency. The empirical results indicate that the banks in FHCs can reduce more costs than the banks not in FHCs, whereas the banks not in FHCs can create greater market value than the banks in FHCs. For the banks joining and not in FHCs, technology gap inefficiency is the main source of inefficiencies in both profitability and marketability processes.     

General convex order on risk aggregation

Using a general notion of convex order, we derive general lower bounds for risk measures of aggregated positions under dependence uncertainty, and this in arbitrary dimensions and for heterogeneous models. We also prove sharpness of the bounds obtained when each marginal distribution has a decreasing density. The main result answers a long-standing open question and yields an insight in optimal dependence structures. A numerical algorithm provides bounds for quantities of interest in risk management. Furthermore, our numerical results suggest that the bounds obtained in this paper are generally sharp for a broader class of models.     

A profit-maximization location-capacity model for designing a service system with risk of service interruptions

This paper considers the design of an immobile service system in which each facility’s service process is subject to the risk of interruptions. The location-capacity decisions and allocations are simultaneously made to maximize the difference between the service provider’s profit and the sum of customers’ transportation and waiting costs. An efficient Lagrangian-based solution algorithm is developed, which solves large-sized instances with up to 50 service facilities and 500 customers in a few seconds. Several sensitivity analyses and managerial insights are presented. The model is also applied to a case study on a logistics network design problem in the zinc mining industry.     

CONVEX RISK MEASURES FOR GOOD DEAL BOUNDS

We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no‐arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent conditions for its existence in terms of market. A good deal valuation is characterized by several equivalent properties and in particular, we see that a convex risk measure is a good deal valuation only if it is given as a risk indifference price. An application to shortfall risk measure is given. In addition, we show that the no‐free‐lunch (NFL) condition is equivalent to the existence of a relevant convex risk measure, which is a good deal valuation. The relevance turns out to be a condition for a good deal valuation to be reasonable. Further, we investigate conditions under which any good deal valuation is relevant.