Portfolio risk analysis of excess of loss reinsurance

Consider a catastrophe insurance market in which primary insurers purchase excess of loss reinsurance to transfer their higher-layer losses to a reinsurer. We conduct a portfolio risk analysis for the reinsurer. In doing so, we model the losses to the primary insurers by a mixture structure, which effectively integrates three risk factors: common shock, systematic risk, and idiosyncratic risk. Assume that the reinsurer holds an initial capital Cn that is in accordance with its market size n. When expanding its business, the reinsurer needs to comply with a certain VaR-based solvency capital requirement, which determines an infimal retention level rn according to the initial capital Cn. As our main results, we find the limit of rn as n→∞ and then establish a weak convergence for the reinsurance portfolio loss. The latter result is applied to approximate the distortion risk measures of the reinsurance portfolio loss. In our numerical studies, we examine the accuracy of the obtained approximations and conduct various sensitivity tests against some risk parameters

The gradient allocation principle based on the higher moment risk measure

According to the gradient allocation principle based on a positively homogeneous and subadditive risk measure, the capital allocated to a sub-portfolio is the Gâteaux derivative, assuming it exists, of the underlying risk measure at the overall portfolio in the direction of the sub-portfolio. We consider the capital allocation problem based on the higher moment risk measure, which, as a generalization of expected shortfall, involves a risk aversion parameter and a confidence level and is consistent with the stochastic dominance of corresponding orders. As the main contribution, we prove that the higher moment risk measure is Gâteaux differentiable and derive an explicit expression for the Gâteaux derivative, which is then interpreted as the capital allocated to a corresponding sub-portfolio. We further establish the almost sure convergence and a central limit theorem for the empirical estimate of the capital allocation, and address the robustness issue of this empirical estimate by computing the influence function of the capital allocation. We also explore the interplay of the risk aversion and the confidence level in the context of capital allocation. In addition, we conduct intensive numerical studies to examine the obtained results and apply this research to a hypothetical portfolio of four stocks based on real data

Forchheimer flow to a well-considering time-dependent critical radius

Previous studies on the non-Darcian flow into a pumping well assumed that critical radius (RCD) was a constant or infinity, where RCD represents the location of the interface between the non-Darcian flow region and Darcian flow region. In this study, a two-region model considering time-dependent RCD was established, where the non-Darcian flow was described by the Forchheimer equation. A new iteration method was proposed to estimate RCD based on the finite-difference method. The results showed that RCD increased with time until reaching the quasi steady-state flow, and the asymptotic value of RCD only depended on the critical specific discharge beyond which flow became non-Darcian. A larger inertial force would reduce the change rate of RCD with time, and resulted in a smaller RCD at a specific time during the transient flow. The difference between the new solution and previous solutions were obvious in the early pumping stage. The new solution agreed very well with the solution of the previous two-region model with a constant RCD under quasi steady flow. It agreed with the solution of the fully Darcian flow model in the Darcian flow region

Numerical Study on Shear Flow in Sliding Bearing with Partial Slip Surface

AbstractFor revealing the effects of slip on such characteristics as friction force and load-bearing capacity of sliding bearing, shear flows of a Newtonian fluid with a varying partial slip surface were computed using finite volume method. Calculation results showed that slip would decrease the friction force, which however was not affected by the location of slip region. The load-bearing capacity of sliding bearing closely depended on the location of slip region, especially the locations of the starting and end points of slip region. A well-designed partial slip surface can improve the load-bearing capacity, otherwise slip would cause lubrication failure

Robust subspace clustering via joint weighted Schatten-p norm and Lq norm minimization

© 2017 SPIE. Low-rank representation (LRR) has been successfully applied to subspace clustering. However, the nuclear norm in the standard LRR is not optimal for approximating the rank function in many real-world applications. Meanwhile, the L21 norm in LRR also fails to characterize various noises properly. To address the above issues, we propose an improved LRR method, which achieves low rank property via the new formulation with weighted Schatten-p norm and Lq norm (WSPQ). Specifically, the nuclear norm is generalized to be the Schatten-p norm and different weights are assigned to the singular values, and thus it can approximate the rank function more accurately. In addition, Lq norm is further incorporated into WSPQ to model different noises and improve the robustness. An efficient algorithm based on the inexact augmented Lagrange multiplier method is designed for the formulated problem. Extensive experiments on face clustering and motion segmentation clearly demonstrate the superiority of the proposed WSPQ over several state-of-the-art methods

Insurance risk analysis of financial networks vulnerable to a shock

We conduct a risk analysis of non-core insurance business of selling protection to financial firms against investment losses due to a shock. A static structural model is constructed, composed of a network of firms who cross-hold each other, a financial market consisting of multiple primitive assets that are vulnerable to a shock, and an insurer who resides external to the network and assesses the opportunity to sell protection to the financial firms. Assume that each firm in the network is rational and able to decide how much protection to purchase to optimize its portfolio according to the mean-variance principle. As a result, the shock may impact on the insurer but indirectly through the network. In view of the robust-yet-fragile nature of financial networks that has been discovered, both empirically and theoretically, by various recent works, one expects that the network integration and the shock play an intertwined role in the insurance risk. Our study forms a theoretical confirmation of this surmise: Depending on the shock size, there are three mutually exclusive scenarios in which an increase in the network integration can either reduce or amplify the impact of the shock on the insurance risk