Abstract. An investigation of the limiting behavior of a risk capital allocation rule based on the Conditional Tail Expectation (CTE) risk measure is carried out. More specifically, with the help of general notions of Extreme Value Theory (EVT), the aforementioned risk capital allocation is shown to be asymptotically proportional to the corresponding Value-atRisk (VaR) risk measure. The existing methodology acquired for VaR can therefore be applied to a somewhat less well-studied CTE. In the context of interest, the EVT approach is seemingly well-motivated by modern regulations, which openly strive for the excessive prudence in determining risk capitals.

This paper presents an extension of the classical compound Poisson risk model for which the inter-claim time and the forthcoming claim amount are no longer independent random variables. Asymptotic tail probabilities for the discounted aggregate claims are presented when the force of interest is constant and the claim amounts are heavy tail distributed random variables. Furthermore, we derive asymptotic finite time ruin probabilities, as well as asymptotic approximations for some common risk measures associated with the discounted aggregate claims.A simulation study is performed in order to validate the results obtained in the free interest risk model.

This is the accepted version of the paper.This version of the publication may differ from the final published version. to allow for an adequate modeling of dependent heavy tailed risks with a non-zero probability of simultaneous loss. Numerous links to certain nowadays existing probabilistic models, as well as seemingly useful characteristic results are proved. Expressions for, e.g., decumulative distribution functions, densities, (joint) moments and regressions are developed. An application to the classical pricing problem is considered, and some formulas are derived using the recently introduced economic weighted premium calculation principles. Permanent repository link

No abstract

The classical problem of identifying the optimal risk transfer from one insurance company to multiple reinsurance companies is examined under some quantilebased risk measure criteria. We develop a new methodology via a two-stage optimisation procedure which allows us to not only recover some existing results in the literature, but also makes possible the analysis of high dimensional problems in which the insurance company diversifies its risk with multiple reinsurance counter-parties, where the insurer risk position and the premium charged by the reinsurers are functions of the underlying risk quantile. Closed form solutions are elaborated for some particular settings, although numerical methods for the second part of our procedure represent viable alternatives for the ease of implementing it in more complex scenarios. Furthermore, we discuss some approaches to obtain more robust results.

This paper studies the set of Pareto optimal insurance contracts and the core of an insurance game. Our setting allows multiple insurers with translation invariant preferences. We characterise the Pareto optimal contracts, which determines the shape of the indemnities. Closed-form and numerical solutions are found for various preferences that the insurance players might have. Determining associated premiums with any given optimal Pareto contract is another problem for which economic-based arguments are further discussed. We also explain how one may link the recent fast growing literature on risk-based optimality criteria to the Pareto optimality criterion and we show that the latter is much more general than the former one, which according to our knowledge, has not been pointed out by now. Further, we extend some of our results when model risk is included, i.e. there is some uncertainty with the risk model and/or the insurance players make decisions based on divergent beliefs about the underlying risk. These robust optimal contracts are investigated and we show how one may find robust and Pareto efficient contracts, which is a key decision-making problem under uncertainty.

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractWe develop portfolio optimization problems for a non-life insurance company seeking to find the minimum capital required, which simultaneously satisfies solvency and portfolio performance constraints. Motivated by standard insurance regulations, we consider solvency capital requirements based on three criteria: Ruin Probability, Conditional Value-at-Risk and Expected Policyholder Deficit ratio. We propose a novel semiparametric formulation for each problem and explore the advantages of implementing this methodology over other potential approaches. When liabilities follow a Lognormal distribution, we provide sufficient conditions for convexity for each problem. Using different expected Return on Capital target levels, we construct efficient frontiers when portfolio assets are modelled with a special class of multivariate GARCH models. We found that the correlation between asset returns plays an important role in the behaviour of the optimal capital required and the portfolio structure. The stability and out-of-sample performance of our optimal solutions are empirically tested with respect to both the solvency requirement and portfolio performance, through a double rolling window estimation exercise.

The optimal reinsurance arrangement is identified whenever the reinsurer counterparty default risk is incorporated in a one-period model. Our default risk model allows the possibility for the reinsurer to fail paying in full the promised indemnity, whenever it exceeds the level of regulatory capital. We also investigate the change in the optimal solution if the reinsurance premium recognises or not the default in payment. Closed form solutions are elaborated when the insurer's objective function is set via some well-known risk measures. It is also discussed the effect of reinsurance over the policyholder welfare. If the insurer is Value-at-Risk regulated, then the reinsurance does not increase the policyholder's exposure for any possible reinsurance transfer, even if the reinsurer may default in paying the promised indemnity. Numerical examples are also provided in order to illustrate and conclude our findings. It is found that the optimal reinsurance contract does not usually change if the counterparty default risk is taken into account, but one should consider this effect in order to properly measure the policyholders's exposure. In addition, the counterparty default risk may change the insurer's ideal arrangement if the buyer and seller have very different views on the reinsurer's recovery rate.