On the discounted aggregate claim costs until ruin in dependent Sparre Andersen risk processes

In this paper, a dependent Sparre Andersen risk process in which the joint density of the interclaim time and the resulting claim severity satisfies the factorization as in Willmot and Woo is considered. We study a generalization of the Gerber–Shiu function (i) whose penalty function further depends on the surplus level immediately after the second last claim before ruin; and (ii) which involves the moments of the discounted aggregate claim costs until ruin. The generalized discounted density with a moment-based component proposed in Cheung plays a key role in deriving recursive defective renewal equations. We pay special attention to the case where the marginal distribution of the interclaim times is Coxian, and the required components in the recursion are obtained. A reverse type of dependency structure, where the claim severities follow a combination of exponentials, is also briefly discussed, and this leads to a nice explicit expression for the expected discounted aggregate claims until ruin. Our results are applied to generate some numerical examples involving (i) the covariance of the time of ruin and the discounted aggregate claims until ruin; and (ii) the expectation, variance and third central moment of the discounted aggregate claims until ruin.     

Claims frequency modeling using telematics car driving data

We investigate the predictive power of covariates extracted from telematics car driving data using the speed-acceleration heatmaps of Gao, G. & Wüthrich, M. V. [(2017). Feature extraction from telematics car driving heatmaps. SSRN ID: 3070069]. These telematics covariates include K-means classification, principal components, and bottleneck activations from a bottleneck neural network. In the conducted case study it turns out that the first principal component and the bottleneck activations give a better out-of-sample prediction for claims frequencies than other traditional pricing factors such as driver's age. Based on these numerical examples we recommend the use of these telematics covariates for car insurance pricing.     

A rating model for loss of profits insurance

Abstract

In this paper we present a rating model for loss of profits insurance for a production system consisting of n production units. Explicit expressions for the company's long run expected average claims expenditures are derived. A numerical example is given.     

Medical chart validation of an algorithm for identifying multiple sclerosis relapse in healthcare claims

Abstract

Objective:

Relapse is a common measure of disease activity in relapsing-remitting multiple sclerosis (MS). The objective of this study was to test the content validity of an operational algorithm for detecting relapse in claims data.

Methods:

A claims-based relapse detection algorithm was tested by comparing its detection rate over a 1-year period with relapses identified based on medical chart review. According to the algorithm, MS patients in a US healthcare claims database who had either (1) a primary claim for MS during hospitalization or (2) a corticosteroid claim following a MS-related outpatient visit were designated as having a relapse. Patient charts were examined for explicit indication of relapse or care suggestive of relapse. Positive and negative predictive values were calculated.

Results:

Medical charts were reviewed for 300 MS patients, half of whom had a relapse according to the algorithm. The claims-based criteria correctly classified 67.3% of patients with relapses (positive predictive value) and 70.0% of patients without relapses (negative predictive value; kappa 0.373: p?<?0.001). Alternative algorithms did not improve on the predictive value of the operational algorithm. Limitations of the algorithm include lack of differentiation between relapsing-remitting MS and other types, and that it does not incorporate measures of function and disability.

Conclusions:

The claims-based algorithm appeared to successfully detect moderate-to-severe MS relapse. This validated definition can be applied to future claims-based MS studies.     

BAYESIAN ANALYSIS OF AGGREGATE LOSS MODELS

This paper describes a Bayesian approach to make inference for aggregate loss models in the insurance framework. A semiparametric model based on Coxian distributions is proposed for the approximation of both the interarrival time between claims and the claim size distributions. A Bayesian density estimation approach for the Coxian distribution is implemented using reversible jump Markov Chain Monte Carlo (MCMC) methods. The family of Coxian distributions is a very flexible mixture model that can capture the special features frequently observed in insurance claims. Furthermore, given the proposed Coxian approximation, it is possible to obtain closed expressions of the Laplace transforms of the total claim count and the total claim amount random variables. These properties allow us to obtain Bayesian estimations of the distributions of the number of claims and the total claim amount in a future time period, their main characteristics and credible intervals. The possibility of applying deductibles and maximum limits is also analyzed. The methodology is illustrated with a real data set provided by the insurance department of an international commercial company.     

关于工程施工索赔浅议

施工索赔对施工单位来说是在非己方过错的情况下对造成的实际损失向业主提出补偿要求。其程序包括:提出索赔要求,报送索赔报告,谈判协商,司法调解,仲裁或起诉。本文主要结合我单位实际情况在施工中常采用的索赔程序进行简要介绍。     

The surplus prior to ruin and the deficit at ruin for a correlated risk process

This paper presents an explicit characterization for the joint probability density function of the surplus immediately prior to ruin and the deficit at ruin for a general risk process, which includes the Sparre-Andersen risk model with phase-type inter-claim times and claim sizes. The model can also accommodate a Markovian arrival process which enables claim sizes to be correlated with the inter-claim times. The marginal density function of the surplus immediately prior to ruin is specifically considered. Several numerical examples are presented to illustrate the application of this result.     

The market value of preventive activities: A contingent-claims approach

We use a contingent-claims approach to determine the market value of preventive investments. We show that the lower the initial probability of accident, the greater is the market value of a reduction in this probability. Besides, at initially low probabilities, ceteris paribus, the market gives a higher value to a reduction in accident probability when aggregate (correlated) catastrophic risks rather than independent ones are involved. The reverse occurs at initially high probabilities.