A Viscosity Solution Theory of Stochastic Hamilton-Jacobi-Bellman equations in the Wasserstein Space

This paper is devoted to a viscosity solution theory of the stochastic Hamilton-Jacobi-Bellman equation in the Wasserstein spaces for the mean-field type control problem which allows for random coefficients and may thus be non-Markovian. The value function of the control problem is proven to be the unique viscosity solution. The major challenge lies in the mixture of the lack of local compactness of the Wasserstein spaces and the non-Markovian setting with random coefficients and various techniques are used, including Ito processes parameterized by random measures, the conditional law invariance of the value function, a novel tailor-made compact subset of measure-valued processes, finite dimensional approximations via stochastic n-player differential games with common noises, and so on.Comment: 41 page

Efficient risk allocation within a non-life insurance group under Solvency II Regime

Intra-group transfers are risk management tools that are usually widely used to optimise the risk position of an insurance group. In this paper, it is shown that premium and liability transfers could be optimally made in such a way as to reduce the amount of Technical Provisions and Minimum Capital Requirement for the entire insurance conglomerate. These levels of required capital represent the minimal amount that needs to be held by the insurance group without regulator intervention, according to the Solvency II regulation. We assume that only proportional risk transfers are feasible, since such transfers are not difficult to administer for a large scaled insurance group, as is always the case. In addition, any risk shifting should be made for commercial purposes in order to be considered acceptable by the local regulators that impose restrictions on how much the assets within an insurance group are fungible. Our numerical examples illustrate the efficiency of the optimal proportional risk transfers which can easily be implemented, in terms of computation, in any well-known solver even for an insurance conglomerate with many subsidiaries. We found that our proposed optimal proportional allocations are more beneficial for large insurance group, since the relative reduction in capital requirement tends to be small, whereas the gain in absolute terms is quite significant for large scaled insurance group

Mediterranean spotted fever in southeastern Romania.

Although cases of Mediterranean spotted fever (MSF) have been reported for decades in southeastern Romania, there are few published data. We retrospectively studied 339 patients, diagnosed with MSF at the National Institute of Infectious Diseases "Prof. Dr. Matei Bals" between 2000 and 2011, in order to raise awareness about MSF in certain regions of Romania. According to the Raoult diagnostic criteria 171 (50.4%) had a score >25 points. Mean age was 52.5 years. One hundred and fifty-five (90.6%) patients were from Bucharest and the surrounding region. Almost all patients presented with fever (99.4%) and rash (98.2%), and 57.9% had evidence of a tick bite. There were no recorded deaths. Serologic diagnosis was made by indirect immunofluorescence assay. Of the 171 patients, serology results for R. conorii were available in 147. One hundred and twenty-three (83.7%) of them had a titer IgG ≥1:160 or a fourfold increase in titer in paired samples. MSF is endemic in southeastern Romania and should be considered in patients with fever and rash even in the absence of recognized tick exposure. Since the disease is prevalent in areas highly frequented by tourists, travel-associated MSF should be suspected in patients with characteristic symptoms returning from the endemic area

Clinical Study Mediterranean Spotted Fever in Southeastern Romania

Although cases of Mediterranean spotted fever (MSF) have been reported for decades in southeastern Romania, there are few published data. We retrospectively studied 339 patients, diagnosed with MSF at the National Institute of Infectious Diseases "Prof. Dr. Matei Bals" between 2000 and 2011, in order to raise awareness about MSF in certain regions of Romania. According to the Raoult diagnostic criteria 171 (50.4%) had a score >25 points. Mean age was 52.5 years. One hundred and fifty-five (90.6%) patients were from Bucharest and the surrounding region. Almost all patients presented with fever (99.4%) and rash (98.2%), and 57.9% had evidence of a tick bite. There were no recorded deaths. Serologic diagnosis was made by indirect immunofluorescence assay. Of the 171 patients, serology results for R. conorii were available in 147. One hundred and twenty-three (83.7%) of them had a titer IgG ≥1 : 160 or a fourfold increase in titer in paired samples. MSF is endemic in southeastern Romania and should be considered in patients with fever and rash even in the absence of recognized tick exposure. Since the disease is prevalent in areas highly frequented by tourists, travel-associated MSF should be suspected in patients with characteristic symptoms returning from the endemic area

Extremes on the discounted aggregate claims in a time dependent risk model

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 (rv's). 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 rv's. 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

Ranking the dietary treatments of broiler chickens in order to reduce nitrogen pollution of the environment

The Analytical Hierarchy Process (AHP) methodology was used to rank the tested nutritional solutions and to choose the best nutritional solution in order to reduce environmental pollution with nitrogen. The evaluation methodology consisted in comparing by three evaluators the diets based on the zootechnical performances/thigh meat quality / environmental impact. The diets of tested nutritional solutions were contained either medicinal and aromatic plants (basil, thyme, sage) in a proportion of 1% (batch 2), respectively essential oils (0.05%) of the same plants (batch 1). The application of the AHP methodology indicated that the best nutritional alternative was obtained for basil, either in the form of essential oil or vegetal material