TVaR-based capital allocation with copulas

Because of regulation projects from control organizations such as the European solvency II reform and recent economic events, insurance companies need to consolidate their capital reserve with coherent amounts allocated to the whole company and to each line of business. The present study considers an insurance portfolio consisting of several lines of risk which are linked by a copula and aims to evaluate not only the capital allocation for the overall portfolio but also the contribution of each risk over their aggregation. We use the tail value at risk (TVaR) as risk measure. The handy form of the FGM copula permits an exact expression for the TVaR of the sum of the risks and for the TVaR-based allocations when claim amounts are exponentially distributed and distributed as a mixture of exponentials. We first examine the bivariate model and then the multivariate case. We also show how to approximate the TVaR of the aggregate risk and the contribution of each risk when using any copula.

On the Moments of the Aggregate Discounted Claims with Dependence Introduced by a FGM Copula

In this paper, we investigate the computation of the moments of the compound Poisson sums with discounted claims when introducing dependence between the interclaim time and the subsequent claim size. The dependence structure between the two random variables is defined by a Farlie-Gumbel-Morgenstern copula. Assuming that the claim distribution has finite moments, we give expressions for the first and the second moments and then we obtain a general formula for any mth order moment. The results are illustrated with applications to premium calculation, moment matching methods, as well as inflation stress scenarios in Solvency II.

The matter distribution in z ~ 0.5 redshift clusters of galaxies. II : The link between dark and visible matter

We present an optical analysis of a sample of 11 clusters built from the EXCPRES sample of X-ray selected clusters at intermediate redshift (z ~ 0.5). With a careful selection of the background galaxies we provide the mass maps reconstructed from the weak lensing by the clusters. We compare them with the light distribution traced by the early-type galaxies selected along the red sequence for each cluster. The strong correlations between dark matter and galaxy distributions are confirmed, although some discrepancies arise, mostly for merging or perturbed clusters. The average M/L ratio of the clusters is found to be: M/L_r = 160 +/- 60 in solar units (with no evolutionary correction), in excellent agreement with similar previous studies. No strong evolutionary effects are identified even if the small sample size reduces the significance of the result. We also provide a individual analysis of each cluster in the sample with a comparison between the dark matter, the galaxies and the gas distributions. Some of the clusters are studied for the first time in the optical.Comment: 25 pages, 9 figues + 11 figures in Annex, 4 tables. Accepted for publication in A&A. 1 reference correcte

Digital Literacy through Presentations at the University Level in Japan

This paper will explain how using student presentations can improve not only language learning but also digital literacy in an English communication course at the university level in Japan. Technology in the classroom can enhance traditional learning by providing access to authentic information since opportunities are scarce in foreign language contexts (Sugino, 2010). In addition, although every student has access to the Internet, few use it to learn information in English, and many lack digital literacy skills (Cote & Milliner, 2016, p. 130). This can be problematic　considering the unavoidable automation of the workplace (and　life in general) in the near future. The solution lays in course　structure, engaging the students beyond the classroom (Benson, 2011), and requiring that students experiment with technology as part of their studies. Results of the questionnaire show that students use the Internet every day for their assignments, and that most perceive the presentations mentioned here as　beneficial for both language and digital literacy skills

A representation-learning approach for insurance pricing with images

Unstructured data are a promising new source of information that insurance companies may use to understand their risk portfolio better and improve the customer experience. However, these novel data sources are difficult to incorporate into existing ratemaking frameworks due to the size and format of the unstructured data. In this paper, we propose a framework to use street view imagery within a generalized linear model. To do so, we use representation learning to extract an embedding vector containing useful information from the image. This embedding is dense and low-dimensional, making it appropriate to use within existing ratemaking models. We find that there is useful information included in street view imagery to predict the frequency of claims for certain types of perils. This model can be used as-is in a ratemaking framework but also opens the door to future empirical research on attempting to extract the causal effect from images that lead to increased or decreased predicted claim frequencies. Throughout, we discuss the practical difficulties (technical and social) of using this type of data for insurance pricing

Sediment Pulses in a Gravel-Bed Flume with Alternate Bars

The proper understanding of gravel-bed river dynamics is a crucial issue for the effective protection against related natural hazards, design of hydraulic structures, and preservation of their high ecological value in mountain regions. However, despite more than one century of research in the field, most available models fail to accurately predict bedload transport rates in such alluvial rivers because of the complex relationships between the flow, channel morphology, and sediment transport. It is now recognized that spatio-temporal variability is an inherent property of bedload transport in gravel-bed rivers which results in its pulsating character even under steady flow conditions. This experimental study aims to better understand the physical mechanisms involved in sediment transport in gravel-bed channels characterized by alternate bars. More specifically, it is concerned with the origins of the pulsating nature of bedload transport under steady external conditions in relation to bed macro-forms. Experiments were conducted over long time periods, in the order of hundreds of hours, in order to investigate transport rate fluctuations over a wide spectrum of time scales and if any dynamic equilibrium state was reached. Three experiments were altogether performed, each characterized by a different sediment feed rate, in a 16-m long and 60-cm wide tilting flume using moderately-sorted gravel. The bedload transport rates were continuously recorded at the flume outlet during the runs using vertical impact plates. Additionally, the bed and water elevations were measured every ten minutes using ultrasonic probes and a laser-sheet imaging technique both mounted on an automated moving cart. The joint analysis of the topographical and bedload transport measurements demonstrated that sediment waves migrated in a step like motion from pool to pool inducing most recorded pulses. They were thus identified as the primary mode of sediment transport in the alternate bar system. Additionally, these migrating low-relief bedforms were found to cause occasional bar failures which generated particularly large pulses. At the largest fluctuation time scale (about 10 h), bedload pulses were associated with quasi-periodic variations in the global bed volume. This observation suggests that the sediment storage capacity of the bed, for a given bed configuration and external conditions, may govern and set an upper limit to the system fluctuations. The comparison between the experiments showed that the bed responded to the increase in sediment supply by increasing its average slope and/or evolving toward a more braided configuration. In addition, this adjustment of the bed transport capacity was found to be associated with a smoothing of the bedload transport pulsating regime resulting in shorter and more frequent pulses of lower magnitude. In conclusion, this study shed new light on bedload transport in gravel-bed rivers by documenting several of its aspects under controlled conditions. More specifically, it bears experimental evidence of the presence of sediment waves in alternate bar systems, and show how the dynamics of these two types of bedform drive sediment transport and control bedload macro-pulse characteristics in gravel-bed channels

High-resolution monitoring of bedload transport rates: a benchmark of two approaches (accelerometers and image processing).

Experimental and field studies have shown how intermittent bedload transport can be at low flow rates. The development and validation of bedload-transport equations require high-resolution records over long periods of time. Two technologies are considered in the present investigation: image processing and accelerometers mounted on impact plates. The former has been successfully applied to monitor bedload transport in many flume experiments, and the latter has shown encouraging results at different field sites. Calibration is a major issue in both cases, and it is often difficult to assess the precision of the data collected. In our talk, we show how to calibrate and compare the performances of accelerometer and image-processing based techniques in laboratory conditions. The accelerometer is fixed on a perforated steel plate, which is placed vertically at the lower end of the flume. The vibrations due to the particles impacting the plate are recorded with a sampling frequency of 10 kHz. The proxy for bedload transport rate is chosen as the number of peaks above a fixed threshold of the recorded signal. Note that impact plates are usually set in flush with the bed, and to our knowledge, the vertical configuration presented here has not yet been documented. The experimental setup for image processing involves a video-camera that takes top-view images of the particles moving over a white board mounted at the outlet of the flume. Data storage poses an issue, which can be got round by pre-processing the images in real time. The bedload transport rate is estimated based on the number of particles that are identified on the images. The two technologies have the advantages of being cost-effective and demanding limited effort for implementation. They provide high-resolution bedload transport rates over several hours. Estimates of bedload discharge were found to be robust and accurate for low sediment transport rates. At higher rates, the sensors may saturate due the arrival of particle clusters. This effect is described and, to a certain degree, taken into account in the calibration relations