Estimation effects on stop-loss premiums under dependence

Even a small amount of dependence in large insurance portfolios can lead to huge errors in relevant risk measures, such as stop-loss premiums. This has been shown in a model where the majority consists of ordinary claims and a small fraction of special claims. The special claims are dependent in the sense that a whole group is exposed to damage. In this model, the parameters have to be estimated. The effect of the estimation step is studied here. The estimation error is dominated by the part of the parameters related to the special claims, because by their nature we do not have many observations of them. Although the estimation error in this way is restricted to a few parameters, it turns out that it may be quite substantial. Upper and lower confidence bounds are given for the stop-loss premium, thus protecting against the estimation effect

The economics of insurance: a review and some recent developments.

The present paper is devoted to different methods of choice under risk in an actuarial setting. The classical expected utility theory is first presented, and its drawbacks are underlined. A second approach based on the so-called distorted expectation hypothesis is then described. It will be seen that the well-known stochastic dominance as well as the stop-loss order have common interpretations in both theories, while defining higher degree stochastic orders leads to different concepts. The aim of this paper is to emphasize the similarities of the two approaches of choice under risk as well as to point out their major differences.Economics; Insurance;

Modeling and comparing dependencies in multivariate risk portfolios

In this paper we investigate multivariate risk portfolios where the risks are dependent. By providing some natural models for risk portfolios with the same marginal distributions we are able to compare two portfolios with different dependence structure with respect to their stoploss premiums. In particular some comparison results for portfolios with twopoint distributions are obtained. The analysis is based on the concept of the so called supermodular ordering. We also give some numerical results which indicate that dependencies in risk portfolios can have a severe impact on the stoploss premium. In fact we show that the effect of dependencies can grow beyond any given bound

Flexible dependence modeling of operational risk losses and its impact on total capital requirements

Operational risk data, when available, are usually scarce, heavy-tailed and possibly dependent. In this work, we introduce a model that captures such real-world characteristics and explicitly deals with heterogeneous pairwise and tail dependence of losses. By considering flexible families of copulas, we can easily move beyond modeling bivariate dependence among losses and estimate the total risk capital for the seven- and eight-dimensional distributions of event types and business lines. Using real-world data, we then evaluate the impact of realistic dependence modeling on estimating the total regulatory capital, which turns out to be up to 38% smaller than what the standard Basel approach would prescrib

Collective Risk-Taking Decisions with Heterogeneous Beliefs

Suppose that a group of agents having divergent expectations can share risks efficiently. We examine how this group should behave collectively to manage these risks. We show that the beliefs of the representative agent is in general a function of the group.s wealth level, or equivalently, that the representative agent has a state-dependent utility function. We define the individual degree of pessimism as an index measuring probability differences across states. We show that the degree of pessimism of the representative agent is the mean of the individual ones weighted by their index of absolute risk tolerance. From this central result, we show how increasing disagreement on the state probability affects the state probability of the representative agent. We show that the divergence of opinions about the probability of occurence of a boom may help solving the equity premium puzzle.aggregation of beliefs, state-dependent utility, efficient risk sharing, pessimism, disagreement, asset pricing, portfolio choices

Risk measurement with the equivalent utility principles.

Risk measures have been studied for several decades in the actuarial literature, where they appeared under the guise of premium calculation principles. Risk measures and properties that risk measures should satisfy have recently received considerable at- tention in the financial mathematics literature. Mathematically, a risk measure is a mapping from a class of random variables defined on some measurable space to the (extended) real line. Economically, a risk measure should capture the preferences of the decision-maker. In incomplete financial markets, prices are no more unique but depend on the agents' attitudes towards risk. This paper complements the study initiated in Denuit, Dhaene & Van Wouwe (1999) and considers several theories for decision under uncertainty: the classical expected utility paradigm, Yaari's dual approach, maximin expected utility theory, Choquet expected utility theory and Quiggin rank-dependent utility theory. Building on the actuarial equivalent utility pricing principle, broad classes of risk measures are generated, of which most classical risk measures appear to be particular cases. This approach shows that most risk measures studied recently in the financial literature disregard the utility concept (i.e. correspond to linear utilities), causing some deficiencies. Some alternatives proposed in the literature are discussed, based on exponential utilities.Actuarial; Coherence; Decision; Expected; Market; Markets; Measurement; Preference; Premium; Prices; Pricing; Principles; Random variables; Research; Risk; Risk measure; Risk measurement; Space; Studies; Theory; Uncertainty; Utilities; Variables;

A concept of copula robustness and its applications in quantitative risk management

In financial and actuarial applications, marginal risks and their dependence structure are often modelled separately. While it is sometimes reasonable to assume that the marginal distributions are ‘known’, it is usually quite involved to obtain information on the copula (dependence structure). Therefore copula models used in practice are quite often only rough guesses. For many purposes, it is thus relevant to know whether certain characteristics derived from d-variate risks are robust with respect to (at least small) deviations in the copula. In this article, a general concept of copula robustness is introduced and criteria for copula robustness are presented. These criteria are illustrated by means of several examples from quantitative risk management. The concept of aggregation robustness introduced by Embrechts et al. (Finance Stoch. 19:763–790, 2015) can be embedded in our framework of copula robustness