A bioinformatics approach to the development of immunoassays for specified risk material in canned meat products

A bioinformatics approach to developing antibodies to specific proteins has been evaluated for the production of antibodies to heat-processed specified risk tissues from ruminants (brain and eye tissue). The approach involved the identification of proteins specific to ruminant tissues by interrogation of the annotation fields within the Swissprot database. These protein sequences were then interrogated for peptide sequences that were unique to the protein. Peptides were selected that met these criteria as close as possible and that were also theoretically resistant to either pepsin or trypsin. The selected peptides were synthesised and used as immunogens to raise monoclonal antibodies. Antibodies specific for the synthetic peptides were raised to half of the selected peptides. These antibodies have each been incorporated into a competitive enzyme-linked immunosorbent assay (ELISA) and shown to be able to detect the heat-processed parent protein after digestion with either pepsin or trypsin. One antibody, specific for alpha crystallin peptide (from bovine eye tissue), was able to detect the peptide in canned meat products spiked with 10% eye tissue. These results, although preliminary in nature, show that bioinformatics in conjunction with enzyme digestion can be used to develop ELISA for proteins in high-temperature processed foods and demonstrate that the approach is worth further study.     

Shrinkage estimators for large covariance matrices in multivariate real and complex normal distributions under an invariant quadratic loss

The problem of estimating large covariance matrices of multivariate real normal and complex normal distributions is considered when the dimension of the variables is larger than the number of samples. The Stein–Haff identities and calculus on eigenstructure for singular Wishart matrices are developed for real and complex cases, respectively. By using these techniques, the unbiased risk estimates for certain classes of estimators for the population covariance matrices under invariant quadratic loss functions are obtained for real and complex cases, respectively. Based on the unbiased risk estimates, shrinkage estimators which are counterparts of the estimators due to Haff [L.R. Haff, Empirical Bayes estimation of the multivariate normal covariance matrix, Ann. Statist. 8 (1980) 586–697] are shown to improve upon the best scalar multiple of the empirical covariance matrix under the invariant quadratic loss functions for both real and complex multivariate normal distributions in the situation where the dimension of the variables is larger than the number of samples.     

The distribution of tax payments in a Lévy insurance risk model with a surplus-dependent taxation structure

We study the distribution of tax payments in the model of Kyprianou and Zhou [Kyprianou, A.E., Zhou, X., 2009. General tax structures and the Lévy insurance risk model. J. Appl. Probab. (in press)], that is a Lévy insurance risk model with a surplus-dependent tax rate. More precisely, after a short discussion on the so-called tax identity, we derive a recursive formula for arbitrary moments of the discounted tax payments until ruin and we identify the distribution of the tax payments when there is no force of interest.     

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.     

The tax identity in risk theory — a simple proof and an extension

By linking queueing concepts with risk theory, we give a simple and insightful proof of the tax identity in the Cramér-Lundberg model that was recently derived in Albrecher & Hipp [Albrecher, H., Hipp, C., 2007. Lundberg’s risk process with tax. Blätter der DGVFM 28 (1), 13-28], and extend the identity to arbitrary surplus-dependent tax rates.     

On the discrete-time compound renewal risk model with dependence

In this paper, we study the discrete-time renewal risk model with dependence between the claim amount random variable and the interclaim time random variable. We consider several dependence structures between the claim amount random variable and the interclaim time random variable. Recursive formulas are derived for the probability mass function and the moments of the total claim amount over a fixed period of time. In the context of ruin theory, explicit expressions for the expected penalty (Gerber-Shiu) function are derived for special cases. We also discuss how the discrete-time compound renewal risk model with dependence can be used to approximate the corresponding continuous time compound renewal risk model with dependence. Numerical examples are provided to illustrate different topics discussed in the paper.     

On a dual model with a dividend threshold

In insurance mathematics, a compound Poisson model is often used to describe the aggregate claims of the surplus process. In this paper, we consider the dual of the compound Poisson model under a threshold dividend strategy. We derive a set of two integro-differential equations satisfied by the expected total discounted dividends until ruin and show how the equations can be solved by using only one of the two integro-differential equations. The cases where profits follow an exponential or a mixture of exponential distributions are then solved and the discussion for the case of a general profit distribution follows by the use of Laplace transforms. We illustrate how the optimal threshold level that maximizes the expected total discounted dividends until ruin can be obtained, and finally we generalize the results to the case where the surplus process is a more general skip-free downwards Lévy process.     

Insurance claims modulated by a hidden Brownian marked point process

Aimed at better modeling insurance claims in an economic environment driven by business cycles, a new Markov-modulated Poisson process model is proposed, and an algorithm is derived to estimate the hidden Markov process by using the observed information. Our method differs from existing ones in the following ways: the new hidden process can model more efficiently the cyclic state of the economic environment; our theory is based on a variation of the law of large numbers and is easy to understand; the Fourier expansion-based parameter estimation algorithm is flexible and can be more easily implemented than other algorithms. Simulation results not only demonstrate the practicality of our model and algorithm, but also show the efficiency and robustness of the estimation algorithm.     

一类相依风险模型的破产问题

本文研究了一类索赔过程与索赔额大小相关的风险模型.利用无穷小方法,得到了该相依模型的折扣惩罚函数的期望满足的方程.及其拉普拉斯变换的表达式.并且给出指数索赔时的具体运用.     

The optimal pricing and ordering policy for an integrated inventory model when trade credit linked to order quantity

In traditional inventory models, it is implicitly assumed that the buyer must pay for the purchased items as soon as they have been received. However, in many practical situations, the vendor is willing to provide the buyer with a permissible delay period when the buyer’s order quantity exceeds a given threshold. Therefore, to incorporate the concept of vendor–buyer integration and order-size-dependent trade credit, we present a stylized model to determine the optimal strategy for an integrated vendor–buyer inventory system under the condition of trade credit linked to the order quantity, where the demand rate is considered to be a decreasing function of the retail price. By analyzing the total channel profit function, we developed some useful results to characterize the optimal solution and provide an iterative algorithm to find the retail price, buyer’s order quantity, and the numbers of shipment per production run from the vendor to the buyer. Numerical examples and sensitivity analysis are given to illustrate the theoretical results, and some managerial insights are also obtained.