Optimal stopping and a non-zero-sum Dynkin game in discrete time with risk measures induced by BSDEs

We first study an optimal stopping problem in which a player (an agent) uses a discrete stopping time in order to stop optimally a payoff process whose risk is evaluated by a (non-linear) g-expectation. We then consider a non-zero-sum game on discrete stopping times with two agents who aim at minimizing their respective risks. The payoffs of the agents are assessed by g-expectations (with possibly different drivers for the different players). By using the results of the first part, combined with some ideas of S. Hamadène and J. Zhang, we construct a Nash equilibrium point of this game by a recursive procedure. Our results are obtained in the case of a standard Lipschitz driver g without any additional assumption on the driver besides that ensuring the monotonicity of the corresponding g-expectation

STUDY ON MINIMUM INHIBITING CONCENTRATION OF ANTIBIOTICS TOWARDS STAPHYLOCOCCUS EPIDERMIDIS STRAINS ISOLATED FROM CLINICAL MATERIALS

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Theoretical and methodical foundations of assessment of foreign economic security of Ukraine Теоретико-методические основы оценки внешнеэкономической безопасности Украины

The article considers problems of assessment of foreign economic security of a country. It proves that when solving the task of analysis, assessment and modelling economic security of a state, the central place belongs to the problem of selection of the system of criteria, which would properly reflect the existing state of economy of states in a specific moment of time. It considers properties of such criteria. It analyses essence of criteria of assessment of foreign economic security. It develops a structural scheme of assessment of foreign economic security of the state, in accordance to which it is offered to consider foreign economic security as a set of three components: trade, financial and investment, and banking and credit ones. It offers a methodical approach to assessment of foreign economic security of the state, which is based on calculation of an integral indicator of security as an arithmetical mean of its components. The proposed approached is used for calculation and analysis of the level of integral indicator of foreign economic security of Ukraine in 2010 – 2011 and study of the dynamics of the level of private indicators of its three components. It builds an equation of linear regression dependence of the integral indicator of foreign economic security of a country on time and it is used as a basis for calculating forecast value of the indicator of foreign economic security of Ukraine for 2012.<br>В статье рассматриваются проблемы оценки внешнеэкономической безопасности страны. Доказано, что при решении задач анализа, оценки и моделирования экономической безопасности государства центральное место занимает проблема выбора системы критериев, которые бы адекватно отражали существующее положение экономики государства в конкретный момент времени. Рассмотрены свойства таких критериев. Проанализирована сущность критериев оценки внешнеэкономической безопасности. Разработана структурная схема оценки внешнеэкономической безопасности государства, согласно которой внешнеэкономическую безопасность предложено рассматривать в совокупности трех составляющих: торговой, финансово-инвестиционной и банковско-кредитной. Предложен методический подход к оценке внешнеэкономической безопасности государства, который базируется на расчете интегрального показателя безопасности как среднеарифметического значения его компонент. На основе предложенного подхода рассчитаны и проанализированы уровень интегрального показателя внешнеэкономической безопасности Украины в 2010 – 2011 годах и исследована динамика уровня частных показателей трех его составляющих. Построено уравнение линейной регрессионной зависимости интегрального показателя внешнеэкономической безопасности страны от времени и на его базе рассчитано прогнозное значение показателя внешнеэкономической безопасности Украины на 2012 год

On the strict value of the non-linear optimal stopping problem

We address the non-linear strict value problem in the case of a general filtration and a completely irregular pay-off process (ξt). While the value process (Vt) of the non-linear problem is only right-uppersemicontinuous, we show that the strict value process (V+t) is necessarily right-continuous. Moreover, the strict value process (V+t) coincides with the process of right-limits (Vt+) of the value process. As an auxiliary result, we obtain that a strong non-linear f-supermartingale is right-continuous if and only if it is right-continuous along stopping times in conditional f-expectation

Optimal stopping with f-expectations: The irregular case

We consider the optimal stopping problem with non-linear f-expectation (induced by a BSDE) without making any regularity assumptions on the payoff process ξ and in the case of a general filtration. We show that the value family can be aggregated by an optional process Y. We characterize the process Y as the Ef-Snell envelope of ξ. We also establish an infinitesimal characterization of the value process Y in terms of a Reflected BSDE with ξ as the obstacle. To do this, we first establish some useful properties of irregular RBSDEs, in particular an existence and uniqueness result and a comparison theorem

BSDEs with Default Jump

We study (nonlinear) Backward Stochastic Differential Equations (BSDEs) driven by a Brownian motion and a martingale attached to a default jump with intensity process λ = (λt). The driver of the BSDEs can be of a generalized form involving a singular optional finite variation process. In particular, we provide a comparison theorem and a strict comparison theorem. In the special case of a generalized λ-linear driver, we show an explicit representation of the solution, involving conditional expectation and an adjoint exponential semimartingale; for this representation, we distinguish the case where the singular component of the driver is predictable and the case where it is only optional. We apply our results to the problem of (nonlinear) pricing of European contingent claims in an imperfect market with default. We also study the case of claims generating intermediate cashflows, in particular at the default time, which are modeled by a singular optional process. We give an illustrating example when the seller of the European option is a large investor whose portfolio strategy can influence the probability of default