Parameter uncertainty and reserve risk under Solvency II

Abstract

In this article we consider the parameter risk in the context of internal modelling of the reserve risk under Solvency II. We discuss two opposed perspectives on parameter uncertainty and point out that standard methods of classical reserving focusing on the estimation error of claims reserves are in general not appropriate to model the impact of parameter uncertainty upon the actual risk of economic losses from the undertakings's perspective. Referring to the requirements of Solvency II we assess methods to model parameter uncertainty for the reserve risk by comparing the probability of solvency actually attained when modelling the solvency risk capital requirement based on the respective method to the required confidence level. Using the simple example of a normal model we show that the bootstrapping approach is not appropriate to model parameter uncertainty according to this criterion. We then present an adaptation of the approach proposed in Fröhlich and Weng (2015). Experimental results demonstrate that this new method yields a risk capital model for the reserve risk achieving the required confidence level in good approximation.

Cyber Loss Model Risk Translates to Premium Mispricing and Risk Sensitivity

“…, n. The minimum value, xmin = x(1,n), is estimated from the data set and hence denoted xmin. As noted in [45] this leads to a biased estimator, however this estimate (17) can be converted to an unbiased version α * as follows [46]:…”

“…Model risk can arise from two different factors: model uncertainty, and parameter uncertainty. While model uncertainty generally refers to the assumptions that one makes in developing a statistical model representation, parameter uncertainty revolves around the idea of predictive inference [17]. In this paper we focus on both aspects of model structure uncertainty as well as parameters uncertainty, and investigate two main channels of transmissions, using the Advisen cyber loss dataset.…”

Alternative Capital Requirement for Insurers: Possibilities and Issues

“…In order to resolve the issue of a short time period, ruin theory and geometric Brownian motion are proposed. In order to resolve deterministic and time issues, the following methods are proposed: bootstrapping (Ohlsson and Lauzeningks, 2009) and stochastic reserving methods, including a Robust Chain Ladder (Peremans et al, 2017), the Fröhlich model (Fröhlich and Weng, 2018), a neural network approach (Hejazi and Jackson, 2017), and a COT method (Dacorogna et al, 2018) developed by the SCOR insurance group.…”

Cyber loss model risk translates to premium mispricing and risk sensitivity

“…Model risk can arise from two different factors: model uncertainty and parameter uncertainty. While model uncertainty generally refers to the assumptions that one makes in developing a statistical model representation, parameter uncertainty revolves around the idea of predictive inference (Fröhlich and Weng 2018 ). In this paper we focus on both aspects of model structure uncertainty as well as parameter uncertainty, and investigate two main channels of transmissions, using the Advisen cyber loss dataset.…”