We show that the rings of constants of generic four-variable Lotka-Volterra derivations are finitely generated polynomial rings. We explicitly determine these rings, and we give a description of all polynomial first integrals of their corresponding systems of differential equations. Besides, we characterize cofactors of Darboux polynomials of arbitrary four-variable Lotka-Volterra systems. These cofactors are linear forms with coefficients in the set of nonnegative integers. Lotka-Volterra systems have various applications in such branches of science as population biology and plasma physics, among many others.
The ring $B(R)$ of all real-valued measurable functions, carrying the pointwise convergence, is a sequential ring completion of the subring $C(R)$ of all continuous functions and, similarly, the ring $\mathbb{B}$ of all Borel measurable subsets of $R$ is a sequential ring completion of the subring $\mathbb{B}_0$ of all finite unions of half-open intervals; the two completions are not categorical. We study $\mathcal L_0^*$-rings of maps and develop a completion theory covering the two examples. In particular, the $\sigma $-fields of sets form an epireflective subcategory of the category of fields of sets and, for each field of sets $\mathbb{A}$, the generated $\sigma $-field $\sigma (\mathbb{A})$ yields its epireflection. Via zero-rings the theory can be applied to completions of special commutative $\mathcal L_0^*$-groups.
The paper studies risk aversion and prudence of an agent in the face of a risk situation with two parameters, one described by a fuzzy number, the other described by a fuzzy variable. The first contribution of the paper is the characterization of risk aversion and prudence in mixed models by conditions on the concavity and the convexity of the agent's utility function and its partial derivatives. The second contribution is the building of mixed models of optimal saving and their connection with the concept of prudence and downside risk aversion.
There is no need to emphasize strongly the economical aspect of energy consumption forecasting in the current conditions of price formation for natural gas distribution companies. Knowledge of the future maximal values of a natural gas load over a day, a week or a month prediction horizon is very important for dispatchers in power distribution companies, who use this information for operating and planning. In our contribution we discuss a possibility to connect the natural gas consumption prediction module with a risk management module. The distribution function of the prediction errors (coming from the prediction module) is estimated and probability P (load > threshold) is derived. The optimal selection of possible regulations of individual consumers is performed by maximizing the economical profit or minimizing the company loss. The number of a possible combination is very large and therefore we use genetic algorithms (GA) as a powerful tool. The results from the two examples are shown: the optimal regulation design strategy (minimal loss) and the optimal gas selling strategy design (maximal profit).
In applications of stochastic programming, optimization of the expected outcome need not be an acceptable goal. This has been the reason for recent proposals aiming at construction and optimization of more complicated nonlinear risk objectives. We will survey various approaches to risk quantification and optimization mainly in the framework of static and two-stage stochastic programs and comment on their properties. It turns out that polyhedral risk functionals introduced in Eichorn and Römisch \cite{Eich-Ro} have many convenient features. We shall complement the existing results by an application of contamination technique to stress testing or robustness analysis of stochastic programs with polyhedral risk objectives with respect to the underlying probability distribution. The ideas will be illuminated by numerical results for a bond portfolio management problem.
This paper presents a study the risk probability optimality for finite horizon continuous-time Markov decision process with loss rate and unbounded transition rates. Under drift condition, which is slightly weaker than the regular condition, as detailed in existing literature on the risk probability optimality Semi-Markov decision processes, we prove that the value function is the unique solution of the corresponding optimality equation, and demonstrate the existence of a risk probability optimization policy using an iteration technique. Furthermore, we provide verification of the imposed condition with two examples of controlled birth-and-death system and risk control, and further demonstrate that a value iteration algorithm can be used to calculate the value function and develop an optimal policy.
In this note attention is focused on finding policies optimizing risk-sensitive optimality criteria in Markov decision chains. To this end we assume that the total reward generated by the Markov process is evaluated by an exponential utility function with a given risk-sensitive coefficient. The ratio of the first two moments depends on the value of the risk-sensitive coefficient; if the risk-sensitive coefficient is equal to zero we speak on risk-neutral models. Observe that the first moment of the generated reward corresponds to the expectation of the total reward and the second central moment of the reward variance. For communicating Markov processes and for some specific classes of unichain processes long run risk-sensitive average reward is independent of the starting state. In this note we present necessary and sufficient condition for existence of optimal policies independent of the starting state in unichain models and characterize the class of average risk-sensitive optimal policies.
This work is concerned with discrete-time Markov stopping games with two players. At each decision time player II can stop the game paying a terminal reward to player I, or can let the system to continue its evolution. In this latter case player I applies an action affecting the transitions and entitling him to receive a running reward from player II. It is supposed that player I has a no-null and constant risk-sensitivity coefficient, and that player II tries to minimize the utility of player I. The performance of a pair of decision strategies is measured by the risk-sensitive (expected) total reward of player I and, besides mild continuity-compactness conditions, the main structural assumption on the model is the existence of an absorbing state which is accessible from any starting point. In this context, it is shown that the value function of the game is characterized by an equilibrium equation, and the existence of a Nash equilibrium is established.
A new genus, Ritacestus, is proposed to accommodate Ritacestus ritaii (Verma, 1926) comb. n. (syn. Proteocephalus ritaii), a parasite of the catfish Rita rita (Hamilton) in India. The new genus, which is placed in the Gangesiinae, is characterized by (i) a small, subspherical scolex formed by four large lobes separated from one another by longitudinal grooves, with a large, widely oval to pyriform rostellum-like apical organ, larger than suckers and possessing an apical hemispherical depression; (ii) paramuscular and cortical position of some vitelline follicles (most follicles are situated medullary); (iii) ventral and dorsal bands of vitelline follicles usually uninterrupted ventral to terminal genitalia and reaching to the posterior margin of proglottides; (iv) the vagina always anterior to the cirrus-sac; (v) a large size of the body (length up to 51 cm); and (vi) development of the uterus of type 2. In its morphology, especially shape of the scolex and apical organ, and paramuscular and cortical position of some vitelline follicles, Ritacestus resembles Postgangesia Akhmerov, 1969, but differs in the presence of a genital atrium (both genital pores of Postgangesia are separate), the anterior position of the vagina (almost always posterior in the latter genus), position of vitelline follicles in cross sections (dorsal and ventral bands in Ritacestus versus only a lateral band in the latter genus), and dorsal excretory canals indistinguishable in mature and gravid proglottides of R. ritaii (well developed in Postgangesia spp.). The type and only species of the genus, R. ritaii, is redescribed on the basis of new material from the type host from the Ganges River basin in India and its neotype is designated.