infonet-economy

This paper illustrates the modeling of dependence structures of non-life insurance risks using the Bernstein copula. We conduct a goodness-of-fit analysis and compare the Bernstein copula with other widely used copulas. Then, we illustrate the use of the Bernstein copula in a value-at-risk and tail-value-at-risk simulation study. For both analyses we utilize German claims data on storm, flood, and water damage insurance for calibration. Our results highlight the advantages of the Bernstein copula, including its flexibility in mapping inhomogeneous dependence structures and its easy use in a simulation context due to its representation as mixture of independent Beta densities. Practitioners and regulators working toward appropriate modeling of dependences in a risk management and solvency context can benefit from our results.

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.

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.

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.

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.

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.

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.

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.

Long-term health insurance contracts provide policyholders with the option of lapsing coverage or switching to another tariff within the same insurance company. We empirically analyze policyholder behavior regarding contract commitment in a large data set of German private health insurance contracts. We show that short-term as well as long-term premium development, along with premium adjustment frequency, affect lapse and tariff switch rates. Moreover, the sales channel has a strong impact on switching behavior, indicating that policyholder choice is not fully independent of sales representatives. Our results are important for risk assessment and risk management of portfolios of health insurance contracts and provide better understanding of the dynamics of policyholder behavior in health insurance.

It is shown that the admissible solutions of the continuity and Bernoulli or Burgers' equations of a perfect one-dimensional liquid are conditioned by a relation established in 1949-1950 by Pauli, Morette, and Van Hove, apparently, overlooked so far, which, in our case, stipulates that the mass density is proportional to the second derivative of the velocity potential. Positivity of the density implies convexity of the potential, i.e., smooth solutions, no shock. Non-elementary and symmetric solutions of the above equations are given in analytical and numerical form. Analytically, these solutions are derived from the original Ansatz proposed in Ref. 1 and from the ensuing operations which show that they represent a particular case of the general implicit solutions of Burgers' equation. Numerically and with the help of an ad hoc computer program, these solutions are simulated for a variety of initial conditions called ldquocompatiblerdquo if they satisfy the Morette-Van Hove formula and ldquoanti-compatiblerdquo if the sign of the initial velocity field is reversed. In the latter case, singular behaviour is observed. Part of the theoretical development presented here is rephrased in the context of the Hopf-Lax formula whose domain of applicability for the solution of the Cauchy problem of the homogeneous Hamilton-Jacobi equation has recently been enlarged.

Fruitful analogies, partially first established by C. M. Newman,(1) between the variables, functions, and equations which describe the equilibrium properties of classical ferro- and antiferromagnets in the Mean Field Approximation (MFA) and those which describe the space-time evolution of compressible Burgers' liquids are developed here for one-dimensional systems. It is shown that the natural analogies are: magnetic field and position coordinate; ferro-/antiferromagnetic coupling constants and negative/positive times; free energy per spin and velocity potential; magnetization and velocity field; magnetic susceptibility and mass density. An unexpected consequence of these analogies is a derivation of the Morette-Van Hove relation. Another novelty is that they necessitate the investigation of weak solutions of Burgers' equation for negative times, corresponding to the Curie-Weiss transition in ferromagnets. This is achieved by solving the ldquofinal-valuerdquo problem of the homogenous Hamilton-Jacobi equation. Unification of the final- and initial-value problems results in an extended Hopf-Lax variational principle. It is shown that its applicability implies that the velocity potentials at time zero be Lipschitz continuous for the velocity field to be bounded. This is a rather mild condition for the class of physically interesting and functionally compatible velocity potentials, compatible in the sense of satisfying the Morette-Van Hove relation.

Results of theoretical and numerical investigations concerning the space-time evolution in 1D of Coulombian and Newtonian systems with densities departing from a uniform and homogeneous background are reported here. In the Coulombian case, the model is called a One Component Plasma. In the Newtonian case, we have the cosmological models of Cold Dark Matter in expanding universes with expansion parameters depending or not upon the cosmological constant. A canonical Hamiltonian formulation is given for studying single-speed solutions of their Coulomb- or Jeans-Vlasov-Poisson descriptions. It is shown that using the Gel'fand mass coordinate the equations of motion are exactly integrable and that the corresponding equations of their characteristics are inhomogeneous, linear and second order ODE's with variable coefficients for the cosmological models. It is furthermore shown that, using correlated initial conditions, Burgers' type of implicit equations for the velocity fields are obtained. Comparison is made between this way to generate exact solutions for the characteristics of the models and that put forward by Zel'dovich. Two examples illustrate the resulting regular and singular mean-field dynamics of the models: a periodic initial excess density for the One Component Plasma and a local departure from homogeneity for the cosmological models.

Results of computer simulations and of theoretical analysis done to investigate and interpret the space-time evolution of the mass density and the velocity field of the inviscid self-gravitating (attractive) and (repulsive) Coulomb liquids in 1D with correlated initial conditions, namely proportionality between the mass density and the divergence of the velocity field are reported here. Numerical data gathered for both models in a collisionless regime reveal an evolution with a time-dependent proportionality factor. Feeding this result in the continuity and div-Euler equations leads to the introduction of another field which is shown to satisfy a Burgers type of implicit equation. A thorough description of regular implosion followed by singular collapses in the attractive case, and of regular explosion in the repulsive case is obtained. Time-inversion symmetry is investigated, energy conservation and stability properties are shown to apply in the regular regions of smooth solutions. The velocity potential satisfies a new local and inhomogeneous PDE.