Cost-of-Capital Margin for a General Insurance Liability Runoff

Under new solvency regulations, general insurance companies need to calculate a risk margin to cover possible shortfalls in their liability runoff. A popular approach for the calculation of the risk margin is the so-called cost-of-capital approach. A comprehensive cost-of-capital approach involves the consideration of multiperiod risk measures. Because multiperiod risk measures are rather complex mathematical objects, various proxies are used to estimate this risk margin. Of course, the use of proxies and the study of their quality raises many questions, see IAA position paper [8]. In the present paper we provide a first discourse on multiperiod solvency considerations for a general insurance liability runoff. Within a chain ladder framework, we derive analytic formulas for the risk margin which allow to compare the comprehensive approach to the different proxies used in practice. Moreover, a case study investigates and answers questions raised in [8

Higher Moments of the Claims Development Result in General Insurance

The claims development result (CDR) is one of the major risk drivers in the profit and loss statement of a general insurance company. Therefore, the CDR has become a central object of interest under new solvency regulation. In current practice, simple methods based on the first two moments of the CDR are implemented to find a proxy for the distribution of the CDR. Such approximations based on the first two moments are rather rough and may fail to appropriately describe the shape of the distribution of the CDR. In this paper we provide an analysis of higher moments of the CDR. Within a Bayes chain ladder framework we consider two different models for which it is possible to derive analytical solutions for the higher moments of the CDR. Based on higher moments we can e.g. calculate the skewness and the excess kurtosis of the distribution of the CDR and obtain refined approximations. Moreover, a case study investigates and answers questions raised in IAS

Benchmarking acid and base dopants with respect to enabling the ice V to XIII and ice VI to XV hydrogen-ordering phase transitions

Doping the hydrogen-disordered phases of ice V, VI and XII with hydrochloric acid (HCl) has led to the discovery of their hydrogen-ordered counterparts ices XIII, XV and XIV. Yet, the mechanistic details of the hydrogen-ordering phase transitions are still not fully understood. This includes in particular the role of the acid dopant and the defect dynamics that it creates within the ices. Here we investigate the effects of several acid and base dopants on the hydrogen ordering of ices V and VI with calorimetry and X-ray diffraction. HCl is found to be most effective for both phases which is attributed to a favourable combination of high solubility and strong acid properties which create mobile H3O+ defects that enable the hydrogen-ordering processes. Hydrofluoric acid (HF) is the second most effective dopant highlighting that the acid strengths of HCl and HF are much more similar in ice than they are in liquid water. Surprisingly, hydrobromic acid doping facilitates hydrogen ordering in ice VI whereas only a very small effect is observed for ice V. Conversely, lithium hydroxide (LiOH) doping achieves a performance comparable to HF-doping in ice V but it is ineffective in the case of ice VI. Sodium hydroxide, potassium hydroxide (as previously shown) and perchloric acid doping are ineffective for both phases. These findings highlight the need for future computational studies but also raise the question why LiOH-doping achieves hydrogen-ordering of ice V whereas potassium hydroxide doping is most effective for the 'ordinary' ice Ih.Comment: 18 pages, 7 figures, 1 tabl

Photoassociation adiabatic passage of ultracold Rb atoms to form ultracold Rb_2 molecules

We theoretically explore photoassociation by Adiabatic Passage of two colliding cold ^{85}Rb atoms in an atomic trap to form an ultracold Rb_2 molecule. We consider the incoherent thermal nature of the scattering process in a trap and show that coherent manipulations of the atomic ensemble, such as adiabatic passage, are feasible if performed within the coherence time window dictated by the temperature, which is relatively long for cold atoms. We show that a sequence of ~2*10^7 pulses of moderate intensities, each lasting ~750 ns, can photoassociate a large fraction of the atomic ensemble at temperature of 100 microkelvin and density of 10^{11} atoms/cm^3. Use of multiple pulse sequences makes it possible to populate the ground vibrational state. Employing spontaneous decay from a selected excited state, one can accumulate the molecules in a narrow distribution of vibrational states in the ground electronic potential. Alternatively, by removing the created molecules from the beam path between pulse sets, one can create a low-density ensemble of molecules in their ground ro-vibrational state.Comment: RevTex, 23 pages, 9 figure

Cloud system resolving model study of the roles of deep convection for photo-chemistry in the TOGA COARE/CEPEX region

International audienceA cloud system resolving model including photo-chemistry (CSRMC) has been developed based on a prototype version of the Weather Research and Forecasting (WRF) model and is used to study influences of deep convection on chemistry in the TOGA COARE/CEPEX region. Lateral boundary conditions for trace gases are prescribed from global chemistry-transport simulations, and the vertical advection of trace gases by large scale dynamics, which is not reproduced in a limited area cloud system resolving model, is taken into account. The influences of deep convective transport and of lightning on NOx, O3, and HOx(=HO2+OH), in the vicinity of the deep convective systems are investigated in a 7-day 3-D 248×248 km2 horizontal domain simulation and several 2-D sensitivity runs with a 500 km horizontal domain. Mid-tropospheric entrainment is more important on average for the upward transport of O3 in the 3-D run than in the 2-D runs, but at the same time undiluted O3-poor air from the marine boundary layer reaches the upper troposphere more frequently in the 3-D run than in the 2-D runs, indicating the presence of undiluted convective cores. In all runs, in situ lightning is found to have only minor impacts on the local O3 budget. Near zero O3 volume mixing ratios due to the reaction with lightning-produced NO are only simulated in a 2-D sensitivity run with an extremely high number of NO molecules per flash, which is outside the range of current estimates. The fraction of NOx chemically lost within the domain varies between 20 and 24% in the 2-D runs, but is negligible in the 3-D run, in agreement with a lower average NOx concentration in the 3-D run despite a greater number of flashes. Stratosphere to troposphere transport of O3 is simulated to occur episodically in thin filaments in the 2-D runs, but on average net upward transport of O3 from below ~16 km is simulated in association with mean large scale ascent in the region. Ozone profiles in the TOGA COARE/CEPEX region are suggested to be strongly influenced by the intra-seasonal (Madden-Julian) oscillation

Modelling tracer transport by a cumulus ensemble: lateral boundary conditions and large-scale ascent

International audienceThe vertical transport of tracers by a cumulus ensemble at the TOGA-COARE site is modelled during a 7 day episode using 2-D and 3-D cloud-resolving setups of the Weather Research and Forecast (WRF) model. Lateral boundary conditions (LBC) for tracers, water vapour, and wind are specified and the horizontal advection of trace gases across the lateral domain boundaries is considered. Furthermore, the vertical advection of trace gases by the large-scale motion (short: vertical large-scale advection of tracers, VLSAT) is considered. It is shown, that including VLSAT partially compensates the calculated net downward transport from the middle and upper troposphere (UT) due to the mass balancing mesoscale subsidence induced by deep convection. Depending on whether the VLSAT term is added or not, modelled domain averaged vertical tracer profiles can differ significantly. Differences between a 2-D and a 3-D model run were mainly attributed to an increase in horizontal advection across the lateral domain boundaries due to the meridional wind component not considered in the 2-D setup

Model sensitivity studies regarding the role of the retention coefficient for the scavenging and redistribution of highly soluble trace gases by deep convective cloud systems

International audienceThe role of the retention coefficient (i.e. the fraction of a dissolved trace gas which is retained in hydrometeors during freezing) for the scavenging and redistribution of highly soluble trace gases by deep convective cloud systems is investigated using a modified version of the Weather Research and Forecasting (WRF) model. Results from cloud system resolving model runs (in which deep convection is initiated by small random perturbations in association with so-called "large scale forcings (LSF)") for a tropical oceanic (TOGA COARE) and a mid-latitude continental case (ARM) are compared to two runs in which bubbles are used to initiate deep convection (STERAO, ARM). In the LSF runs, scavenging is found to almost entirely prevent a highly soluble tracer initially located in the lowest 1.5 km of the troposphere from reaching the upper troposphere, independent of the retention coefficient. The release of gases from freezing hydrometeors leads to mixing ratio increases in the upper troposphere comparable to those calculated for insoluble trace gases only in the two runs in which bubbles are used to initiate deep convection. A comparison of the two ARM runs indicates that using bubbles to initiate deep convection may result in an overestimate of the influence of the retention coefficient on the vertical transport of highly soluble tracers. It is, however, found that the retention coefficient plays an important role for the scavenging and redistribution of highly soluble trace gases with a (chemical) source in the free troposphere and also for trace gases for which even relatively inefficient transport may be important. The large difference between LSF and bubble runs is attributed to differences in dynamics and microphysics in the inflow regions of the storms. The dependence of the results on the model setup indicates the need for additional model studies with a more realistic initiation of deep convection, e.g., considering effects of orography in a nested model setup

Market value margin via mean-variance hedging

We use mean–variance hedging in discrete time in order to value an insurance liability. The prediction of the insurance liability is decomposed into claims development results, that is, yearly deteriorations in its conditional expected values until the liability is finally settled. We assume the existence of a tradeable derivative with binary pay-off written on the claims development result and available in each development period. General valuation formulas are stated and, under additional assumptions, these valuation formulas simplify to resemble familiar regulatory cost-of-capital-based formulas. However, adoption of the mean–variance framework improves upon the regulatory approach by allowing for potential calibration to observed market prices, inclusion of other tradeable assets, and consistent extension to multiple periods. Furthermore, it is shown that the hedging strategy can also lead to increased capital efficiency