The problem of designing an optimal insurance strategy in a modification of the risk process with discrete time is investigated. This model introduces stage-by-stage probabilistic constraints ...(Value-at-Risk (VaR) constraints) on the insurer's capital increments during each stage. Also, the set of admissible insurances is determined by a safety level reflecting a 'good' or 'bad' capital increment at the previous stage. The mathematical expectation of the insurer's final capital is used as the objective functional. The total loss of the insurer at each stage is modeled by the Gaussian (normal) distribution with parameters depending on a seded loss function (or, in other words, an insurance policy) selected. In contrast to traditional dynamic optimization models for insurance strategies, the proposed approach allows to construct the value functions (and hence the optimal insurance policies) by simply solving a sequence of static insurance optimization problems. It is demonstrated that the optimal seded loss function at each stage depends on the prescribed value of the safety level: it is either a stop-loss insurance or conditional deductible insurance having a discontinuous point. In order to reduce ex post moral hazard, we also investigate the case, where both parties in an insurance contract are obligated to pay more for a larger realization of loss. This leads to that the optimal seeded loss functions are either stop-loss insurances or unconditional deductible insurances.
The problem of designing an optimal insurance strategy in a new multistep insurance model is investigated. This model introduces stepwise probabilistic constraints (Value-at-Risk constraints) on the ...insurer’s capital, i.e., probabilistic constraints on the insurer’s capital increments during one step. As the objective functional the mathematical expectation of the insurer’s final capital is used. The total damage to the insurer at each step is modeled by the Gaussian distribution with parameters depending on a risk sharing function selected. In contrast to traditional dynamic optimization models for insurance strategies, the approach proposed below takes into account stepwise constraints; within this approach, the Bellman functions are constructed (and hence the optimal risk sharing is found) by simply solving a sequence of static insurance optimization problems. It is demonstrated that the optimal risk sharing is the so-called stop-loss insurance.
•A kinetic model of biochemical reactions in a potentiometric enzyme biosensor is proposed.•Biochemical reaction rates in the bioselective membrane are evaluated through fitting the biosensor ...response.•Sensitivity of biosensor response to the biochemical reaction rates is investigated.
We have investigated the operation of a potentiometric biosensor based on reversible acetylcholinesterase inhibition for determination of aflatoxin B1. The biochemical reactions between enzyme, substrate, and inhibitor are described using rate equations. A sensitivity study of the biosensor response to the biochemical reaction rates was done by varying each rate constant. The response to substrate and inhibitor was used as a fitting target for evaluation of the biochemical reaction rates. Initial concentrations of the enzyme (2.0 × 10−5 M acetylcholinesterase), the substrate (4.0 × 10−3 M acetylcholine chloride), and the inhibitor (9.6 × 10−6 M aflatoxin B1) in the biosensor membrane act as the boundary conditions for the rate equations. This kinetic model allowed us to establish the effect of reaction rates on the biosensor response and reproduce the response to different inhibitor concentrations. The results may be used for biosensor design and optimization.
The paper presents a constructive description of the set of all efficient (Pareto-optimal) investment portfolios in a new setting, where the risk measure named “shortfall probability” (SP) is ...understood as the probability of a shortfall of investor’s capital below a prescribed level. Under a normality assumption, it is shown that SP has a generalized convexity property, the set efficient portfolios is constructed. Relations between the set of mean-SP and the set of mean-variance efficient portfolios as well as between mean-SP and mean-Value-at-Risk (VaR) sets of efficient portfolios are studied. It turns out that mean-SP efficient set is a proper subset of the mean-variance efficient set; interrelation with the mean-VaR efficient set is more complicated, however, mean-SP efficient set is proved to be a proper subset of mean-VaR efficient set under a sufficiently high confidence level. Besides a normal distribution, elliptic distributions are considered as an alternative for modeling the investor’s total return distribution. The obtained results provides the investor with a risk measure, that is more vivid than the variance and Value-at-Risk, and with determination of the corresponding set of effective portfolios.
We solve a problem of optimal risk control in the static model by choosing an admissible insurance policy, where the objective functional is the so-called Markowitz utility functional, i.e., a ...functional that depends only on the mean value and standard deviation of the insurer’s final capital after an insurance transaction. Interests of the insurer are taken into account by introducing probabilistic or, more precisely, quantile constraints (value at risk constraint) on the final capital of the insurer, using a normal distribution to model the distribution of total damage. Additionally, we impose a restriction with probability one on the risk taken from an individual policy holder. Optimal from the point of view of the insurer is the so-called stop-loss insurance. We find explicit forms of conditions for refusing an insurance transaction. We give an example that illustrates the proven results in case of an exponential distribution of claim size.
As a representative of a common carbon‐bearing hot work tool steel AISI H13 is in focus of the present review paper. Most relevant details for processing of AISI H13 by laser powder bed fusion ...(L‐PBF) are systematically investigated. Three common stages of process parameter development and material assessment, respectively, are in focus: general processibility, process refinement, and deduction of process–microstructure–property relations, i.e., understanding of the interplay of relevant elementary mechanisms. On the one hand, the routine of AISI H13 processing by L‐PBF is optimized for industrial application. This optimization includes laser parameters, heat treatment, and process sensitivity concerning the used machine and powder. On the other hand, the cluster‐like melt pool microstructure and the formation of various defects during L‐PBF processing of AISI H13 powder are under investigation. Most importantly, understanding of solidification cracking based on critical temperature regimes and residual stress cracking related to martensitic transformation is essential for robust process and material development for the L‐PBF process.
A literature review complemented by systematic experiments focusing on AISI H13 processed by laser powder bed fusion is presented. Process–microstructure–property relations are established, considering powder properties, preheating temperature, laser parameters, and heat treatment. Based on experiments focusing on various steels used for tooling, different types of defects are highlighted and rationalized based on underlying elementary mechanisms.
Construction of geologic and hydrodynamic models of carbonate reservoirs in the conditions of information lack about fracture parameters is always connected with the high degree of uncertainty. In ...the article the approach to the studying and the prediction of fracture of the carbonate reservoir based on the distribution and the trending of tectonic stress in the region of the researching object is presented. As illustrated by one of the field of the Eastern Caucasus the geotectonic description of the territory is listed, the fracture parameters on the indirect data were received, the zones of the increased productivity (fracturing) of reservoirs were highlighted and the modeling of fractures was held in Petrel software.
Methods for constructing distributed automation systems for circuit design to calculate the instability of the coordinates of the operating points of the static mode of nonlinear electronic circuits ...were considered. Two-terminal networks of type
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and transmission parameters of dependent sources, as well as characteristics of external influences (temperature, radiation, etc.) are taken as components that change under the influence of external factors. To solve the problem of calculating the instability of the coordinates of the operating points of the static mode of nonlinear electronic circuits, a technique is proposed based on the use of an auxiliary circuit, which is constructed by transposing the description of the original circuit. The features of the organization of serverless and microservice architecture for building circuit design automation systems are analyzed. The multitenant design of a microservice information system environment is described. The mechanism of operation of the service as a service is presented to ensure the operation of the business logic of the server component.
The production of special interior contoured tools made of cemented carbide is a time- and cost-intensive multistage sintering process. An alternative for economic, flexible and automated production ...is provided by a laser-based, additive manufacturing Selective Laser Melting process (SLM). In a shortened process chain near-net-shape and special interior contoured tools can be manufactured energy- and resource-efficiently in small batch sizes. An increase of the tool life is achieved by the use of wear resistant and tough cemented carbide material. This paper focusses on the process behavior of the agglomerated and pre-sintered tungsten carbide-cobalt (WC-Co) powder material in the SLM process. Depending on the exposure parameters, various types of micro structures can be generated and the original material profile can be significantly changed during the laser material interaction.
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