Mack's estimator motivated by large exposure asymptotics in a compound Poisson setting
The distribution-free chain ladder of Mack justified the use of the chain ladder predictor and enabled Mack to derive an estimator of conditional mean squared error of prediction for the chain ladder predictor. Classical insurance loss models, i.e. of compound Poisson type, are not consistent with Mack's distribution-free chain ladder. However, for a sequence of compound Poisson loss models indexed by exposure (e.g. number of contracts), we show that the chain ladder predictor and Mack's estimator of conditional mean squared error of prediction can be derived by considering large exposure asymptotics. Hence, quantifying chain ladder prediction uncertainty can be done with Mack's estimator without relying on the validity of the model assumptions of the distribution-free chain ladder.
Code (0)
등록된 구현이 없습니다.
Tasks
PredictionSimilar Papers 제목 키워드 기반
Causal Inference Under Approximate Neighborhood Interference
This paper studies causal inference in randomized experiments under network interference. Commonly used models of interference posit that treatments assigned to alters beyond a certain network distance from the ego have …
Causal InferenceLedoit-Wolf linear shrinkage with unknown mean
This work addresses large dimensional covariance matrix estimation with unknown mean. The empirical covariance estimator fails when dimension and number of samples are proportional and tend to infinity, settings known as…
Precise High-Dimensional Asymptotics for Quantifying Heterogeneous Transfers
The problem of learning one task with samples from another task is central to transfer learning (TL). In this paper, we examine a fundamental question: When does combining the data samples from a source task and a target…
Multi-Task Learningtext-classificationText ClassificationTransfer LearningSmall-time asymptotics for Gaussian self-similar stochastic volatility models
We consider the class of self-similar Gaussian stochastic volatility models, and compute the small-time (near-maturity) asymptotics for the corresponding asset price density, the call and put pricing functions, and the i…
Higher-order Refinements of Small Bandwidth Asymptotics for Density-Weighted Average Derivative Estimators
The density weighted average derivative (DWAD) of a regression function is a canonical parameter of interest in economics. Classical first-order large sample distribution theory for kernel-based DWAD estimators relies on…