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Oct 28, 2016 · In the chain ladder model of Schnaus, the chain ladder predictors are unbiased. This result is remarkable since unbiasedness of the chain ladder predictors is an open question in other stochastic models leading to the chain ladder method.
- Klaus Th. Hess, Klaus D. Schmidt, Anja Schnaus
- 2016
Dec 20, 2002 · In Section 6 we consider two models in which the aforementioned variations of the chain–ladder method can be compared by certain optimality criteria. In these models, optimal prediction yields the chain–ladder predictors of the non-observable aggregate claims.
- Klaus Th. Hess, Klaus D. Schmidt
- 2002
Using the chain ladder predictors of the future cumulative losses, we define the chain ladder predictors ZCL i,k:= SCL i,n− +1 − S i,n−i if i +k = n +1 SCL i,k − S CL i,k−1 else of the future incremental losses Z i,k and the chain ladder predictors RCL i:= n l=n−i+1 ZCL i,l RCL (c):= n l=c−n ZCL c−l,l RCL:= n l=1 n j=n−l+1 ...
- Klaus D. Schmidt
- 2016
In the present paper, we propose a multivariate model which extends the univariate model of Schnaus, presented in Schmidt and Schnaus [1996], and the bivariate model of Braun [2004].
2.2 Univariate Chain{Ladder Model Let us now consider the univariate chain{ladder model due to Schnaus which was proposed by Schmidt and Schnaus [1996] and is a slight but convenient extension of the model of Mack [1993]. The chain{ladder model is a sequential model since it involves successive condition-
Oct 28, 2016 · For every accident year i and every development year k such that \( i+k \) \( \ge n+1 \), the future cumulative loss \( S_{i,k} \) is predicted by the chain ladder predictor $$\begin{aligned} S_{i,k}^\mathrm{CL}:= & {} S_{i,n-i} \prod _{l=n-i+1}^k \varphi _l^\mathrm{CL}\end{aligned}$$
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a model in which the chain ladder predictor of ultimate aggregate claims turns out to be unbiased. 1. INTRODUCTION The chain ladder method is a simple and suggestive tool in claims reserving, and vari-ous attempts have been made aiming at its justification in a stochastic model. Remar-
