Dorothea Diers, Martin Eling and Marc Linde
The purpose of this paper is to illustrate the importance of modeling parameter risk in premium risk, especially when data are scarce and a multi‐year projection horizon is…
Abstract
Purpose
The purpose of this paper is to illustrate the importance of modeling parameter risk in premium risk, especially when data are scarce and a multi‐year projection horizon is considered. Internal risk models often integrate both process and parameter risks in modeling reserve risk, whereas parameter risk is typically omitted in premium risk, the modeling of which considers only process risk.
Design/methodology/approach
The authors present a variety of methods for modeling parameter risk (asymptotic normality, bootstrap, Bayesian) with different statistical properties. They then integrate these different modeling approaches in an internal risk model and compare their results with those from modeling approaches that measure only process risk in premium risk.
Findings
The authors show that parameter risk is substantial, especially when a multi‐year projection horizon is considered and when there is only limited historical data available for parameterization (as is often the case in practice). The authors' results also demonstrate that parameter risk substantially influences risk‐based capital and strategic management decisions, such as reinsurance.
Practical implications
The authors' findings emphasize that it is necessary to integrate parameter risk in risk modeling. Their findings are thus not only of interest to academics, but of high relevance to practitioners and regulators working toward appropriate risk modeling in an enterprise risk management and solvency context.
Originality/value
To the authors' knowledge, there are no model approaches or studies on parameter uncertainty for projection periods of not just one, but several, accident years; however, consideration of multiple years is crucial when thinking strategically about enterprise risk management.
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The purpose of this paper is to illustrate how risk capital can be calculated and allocated in a multi‐year context. This is an important issue, since strategic management and…
Abstract
Purpose
The purpose of this paper is to illustrate how risk capital can be calculated and allocated in a multi‐year context. This is an important issue, since strategic management and decision making within insurance companies require a multi‐year time horizon (instead of a one‐year time horizon, as set out in solvency models).
Design/methodology/approach
After defining risk capital in a multi‐year context, the paper discusses the different properties of the multi‐year risk capital concept. The paper also presents an allocation rule of how to allocate the multi‐year risk capital to individual years as well as to individual segments. The paper applies the author's model framework in an application study to illustrate the different effects.
Findings
The paper shows how multi‐year risk capital can be used as a basis for analyzing different management strategies within risk and return indicators in the context of value‐based management. Furthermore, the paper demonstrates the effect of allocating risk capital in a multi‐year context.
Originality/value
The analysis provides new and relevant information to insurance companies' management. Whereas usually solvency rules set out a time horizon of one year, in the context of internal risk models a multi‐year planning horizon is taken into account. Management needs to get an idea of how much risk capital is necessary in order to survive the next five years without external capital supply. The paper presents an answer to these questions.
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Dorothea Diers, Martin Eling, Christian Kraus and Marc Linde
The purpose of this paper is to present a simulation‐based approach for modeling multi‐year non‐life insurance risk in internal risk models. Strategic management in an insurance…
Abstract
Purpose
The purpose of this paper is to present a simulation‐based approach for modeling multi‐year non‐life insurance risk in internal risk models. Strategic management in an insurance company requires a multi‐year time horizon for economic decision making, for example, in the context of internal risk models. In the literature to date, only the ultimate perspective and, more recently, the one‐year perspective (for Solvency II purposes) are considered.
Design/methodology/approach
The authors present a way of defining and calculating multi‐year claims development results and extend the simulation‐based algorithm (“re‐reserving”) for quantifying one‐year non‐life insurance risk, presented in Ohlsson and Lauzeningks, to a multi‐year perspective.
Findings
The multi‐year algorithm is applied to the chain ladder reserving model framework of Mack (1993).
Practical implications
The usefulness of the new multi‐year horizon is illustrated in the context of internal risk models by means of a case study, where the multi‐year algorithm is applied to a claims development triangle based on Mack and on England and Verrall. This algorithm has been implemented in an excel tool, which is given as supplemented material.
Originality/value
To the best of the authors' knowledge, there are no model approaches or studies on insurance risk for projection periods of not just one, but several, new accident years; this requires a suitable extension of the classical Mack model; however, consideration of multiple years is crucial in the context of enterprise risk management.
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Dorothea Diers, Martin Eling, Christian Kraus and Andreas Reuß
The purpose of this paper is to transfer the concept of market‐consistent embedded value (MCEV) from life to non‐life insurance. This is an important undertaking since differences…
Abstract
Purpose
The purpose of this paper is to transfer the concept of market‐consistent embedded value (MCEV) from life to non‐life insurance. This is an important undertaking since differences in management techniques between life and non‐life insurance make management at the group level very difficult. The purpose of this paper is to offer a solution to this problem.
Design/methodology/approach
After explaining MCEV, the authors derive differences between life and non‐life insurance and develop a MCEV model for non‐life business. The model framework is applied to a German non‐life insurance company to illustrate its usefulness in different applications.
Findings
The authors show an MCEV calculation based on empirical data and set up an economic balance sheet. The value implications of varying loss ratios, cancellation rates, and costs within a sensitivity analysis are analyzed. The usefulness of the model is illustrated within a value‐added analysis. The authors also embed the MCEV concept in a simplified model for an insurance group, to derive group MCEV and outline differences between local GAAP, IFRS and MCEV.
Practical implications
The analysis provides new and relevant information to the stakeholders of an insurance company. The model provides information comparable to that provided by embedded value models currently used in the life insurance industry and fills a gap in the literature. The authors reveal significant valuation difference between MCEV and IFRS and argue that there is a need for a consistent MCEV approach at the insurance‐group level.
Originality/value
The paper presents a new valuation technique for non‐life insurance that is easy to use, simple to interpret, and directly comparable to life insurance. Despite the growing policy interest in embedded value, not much academic attention has been given to this methodology. The authors hope that this work will encourage further discussion on this topic in academia and practice.