New Issue of Variance Forthcoming
The fifth issue of Variance: Advancing the Science of Risk is forthcoming. The complete text of the articles described below will be accessible online at www.VarianceJournal.org.
“Capital Allocation by Percentile Layer” by Neil Bodoff describes a new approach to capital allocation. The catalyst for the new approach is a new formulation of the meaning of holding Value at Risk (VaR) capital that expresses the firm’s total capital as the sum of many granular pieces of capital, or “percentile layers of capital.” As a result, one must allocate capital separately to each layer and perform the capital allocation across all layers. Ultimately, on the practical plane, capital allocation by percentile layer produces allocations that are different from many other methods. At the same time, on the theoretical plane, capital allocation by percentile layer leads to new continuous formulas for risk load and utility.
In “A Top-Down Approach to Understanding Parameter Uncertainty in Loss Ratio Estimation” Alice Underwood and Jian-An Zhu define a specific measure of error in the estimation of loss ratios; specifically, the authors focus on the discrepancy between the original estimate of the loss ratio and the ultimate value of the loss ratio. They also investigate what publicly available data can tell us about this measure.
“Property-Liability Insurance Loss Reserve Ranges Based on Economic Value” by Stephen P. D’Arcy, Alfred Au, and Liang Zhang combines loss reserve variability and economic valuation. Loss reserve ranges are calculated on a nominal and economic basis for a simplified insurer to illustrate the key variables that impact loss reserve variability.
“Theory and Practice of Timeline Simulation” by Rodney Kreps discusses simulation in a timeline formulation in theory and practice. It is shown that all the usual simulation results can be obtained and many new forms can be expressed simply. The paper argues that this procedure is more intuitive, physically more real, and technically more correct than the collective risk model.
“The Chain Ladder and Tweedie Distributed Claims Data” by Greg Taylor considers a model with multiplicative accident period and development period effects, and derives the ML equations for parameter estimation in the case that the distribution of each cell of the claims triangle is a general member of the Tweedie family. This yields some known special cases, e.g., over-dispersed Poisson (ODP) distribution (Tweedie parameter p=1), for which the chain ladder algorithm is known to provide maximum likelihood (ML) parameter estimates, and gamma distribution (p=2). The intermediate cases (1 < p < 2) represent compound Poisson cell distributions with gamma severity distributions. While ML estimates are not chain ladder for Tweedie distributions other than ODP, the paper investigates why they will be close to chain ladder under certain circumstances.
“Adaptive Reserving Using Bayesian Revision for the Exponential Dispersion Family” by Greg Taylor and Gráinne McGuire investigates the practical aspects of applying the second-order Bayesian revision of a generalized linear model (GLM) to form an adaptive filter for claims reserving. It discusses the application of such methods to three typical models used in Australian general insurance circles and considers extensions, including the application of bootstrapping to an adaptive filter and the blending of results from the three models.
In “Prediction Error of the Multivariate Additive Loss Reserving Method for Dependent Lines of Business,” Michael Merz and Mario Wüthrich point out that, often, in non-life insurance, claims reserves are the largest position on the liability side of the balance sheet, and so the prediction of adequate claims reserves for a portfolio consisting of several run-off subportfolios from dependent lines of business is of great importance for every non-life insurance company.
The authors consider the claims reserving problem in a multivariate context, studying a special case of the multivariate additive loss reserving model proposed by Hess, Schmidt, and Zocher (2006) and Schmidt (2006). This model allows for a simultaneous study of the individual run-off subportfolios and enables the derivation of an estimator for the conditional mean square error of prediction (MSEP) for the predictor of the ultimate claims of the total portfolio.