VTeX: Solutions for Science Publishing

A single jump filtration ${({\mathcal{F}_{t}})_{t\in {\mathbb{R}_{+}}}}$ generated by a random variable γ with values in ${\overline{\mathbb{R}}_{+}}$ on a probability space $(\Omega ,\mathcal{F},\mathsf{P})$ is defined as follows: a set $A\in \mathcal{F}$ belongs to ${\mathcal{F}_{t}}$ if $A\cap \{\gamma >t\}$ is either ∅ or $\{\gamma >t\}$. A process M is proved to be a local martingale with respect to this filtration if and only if it has a representation ${M_{t}}=F(t){\mathbb{1}_{\{t<\gamma \}}}+L{\mathbb{1}_{\{t\geqslant \gamma \}}}$, where F is a deterministic function and L is a random variable such that $\mathsf{E}|{M_{t}}|<\infty $ and $\mathsf{E}({M_{t}})=\mathsf{E}({M_{0}})$ for every $t\in \{t\in {\mathbb{R}_{+}}:\mathsf{P}(\gamma \geqslant t)>0\}$. This result seems to be new even in a special case that has been studied in the literature, namely, where $\mathcal{F}$ is the smallest σ-field with respect to which γ is measurable (and then the filtration is the smallest one with respect to which γ is a stopping time). As a consequence, a full description of all local martingales is given and they are classified according to their global behaviour.

A new multi-factor short rate model is presented which is bounded from below by a real-valued function of time. The mean-reverting short rate process is modeled by a sum of pure-jump Ornstein–Uhlenbeck processes such that the related bond prices possess affine representations. Also the dynamics of the associated instantaneous forward rate is provided and a condition is derived under which the model can be market-consistently calibrated. The analytical tractability of this model is illustrated by the derivation of an explicit plain vanilla option price formula. With view on practical applications, suitable probability distributions are proposed for the driving jump processes. The paper is concluded by presenting a post-crisis extension of the proposed short and forward rate model.

A general class of probability density functions is considered, containing as particular case the Barenblatt solutions arising, for instance, in the study of nonlinear heat equations. Alternative probabilistic representations of the Barenblatt-type solutions $u(x,t)$ are proposed. In the one-dimensional case, by means of this approach, $u(x,t)$ can be connected with the wave propagation.

The existence and uniqueness are proved for the global positive solution to the system of stochastic differential equations describing a two-species mutualism model disturbed by the white noise, the centered and non-centered Poisson noises. We obtain sufficient conditions for stochastic ultimate boundedness, stochastic permanence, nonpersistence in the mean, strong persistence in the mean and extinction of the solution to the considered system.

In this paper we investigate a problem of large deviations for continuous Volterra processes under the influence of model disturbances. More precisely, we study the behavior, in the near future after T, of a Volterra process driven by a Brownian motion in a case where the Brownian motion is not directly observable, but only a noisy version is observed or some linear functionals of the noisy version are observed. Some examples are discussed in both cases.

Generalizing earlier work of Delbaen and Haezendonck for given compound renewal process S under a probability measure P we characterize all probability measures Q on the domain of P such that Q and P are progressively equivalent and S remains a compound renewal process under Q. As a consequence, we prove that any compound renewal process can be converted into a compound Poisson process through a change of measures and we show how this approach is related to premium calculation principles.

We analyze almost sure asymptotic behavior of extreme values of a regenerative process. We show that under certain conditions a properly centered and normalized running maximum of a regenerative process satisfies a law of the iterated logarithm for the lim sup and a law of the triple logarithm for the lim inf. This complements a previously known result of Glasserman and Kou [Ann. Appl. Probab. 5(2) (1995), 424–445]. We apply our results to several queuing systems and a birth and death process.

The Nordic Baltic region (5+3)2 is now closely interlinked via trade, investment, mobility of people, and banking. All the countries in this group have pursued some form of integration with the European Union (EU). Six of them are EU member states, four of them are members of the euro area, and all of them are within the European Economic Area (EEA) and are Schengen member states. But can these small countries as a group cooperate more closely and perhaps exercise more collective authority in Europe? The Nordic countries and the Baltic States cooperate in the Bretton Woods institutions, the World Bank and the IMF, and six of them are among European NATO member states. When it comes to European integration the lack of common approach complicates their cooperation. Within this group there are internal divisions between the hardcore EU and euro area member states (the Baltics and Finland), EU members (Denmark and Sweden) and EU outsiders (Iceland and Norway). Common pathways for the future cooperation in Europe may be hard to find. Also, the Nordics are high income welfare states, but the Baltics are neoliberal with minimal governments and low-tax regimes. Additionally, external forces continue to challenge the Nordic Baltic region, including revanchist Russian policies threatening Baltic Sovereignty, unpredictable US policies towards NATO as well as reduced military presence in Europe, and dismal EU and euro area post crisis economic performance. All point to a future of uncertainty including both economic and security risks.

The paper is part of a research series for ancient Roman sites in Northern Bulgaria which aim to present the possibilities of creating a specialized form of cultural and historical product that ensures sustainable utilization of the Bulgarian tangible heritage. A study of the Roman fortress Sostra, located on the Via Traiani road as a cultural and historical tourist resource was conducted. The castellum is characterized as an object of cultural heritage in the region of Troyan Municipality in Bulgaria. The methodology applied in assessing the potential of the Ancient Roman fortress Sostra is primarily designed for historical and cultural sites. An evaluation was made under the following criteria: potential for development, degree of impact / interaction, degree of modification with relevant indicators. Also an expedition-field method for terrain research was applied. Summaries and conclusions were made in order to highlight the possibility of forming a tourist product of cultural and cognitive tourism.

This time, the journal is publishing articles of different scientific interests. The articles are different, as is the autumn colour palette in nature. H. Hilmarrson provided insights into the economic similarities and differences between the Nordic and Baltic countries, while A. Guogis, A. V. Rakšnys analyzed patterns of welfare states. The prosperity of the state cannot exist if there is corruption in the country. And perception of corruption was investigated by I. Pikturnaitė, J. Jonuševičienė, R. Kavolius. The analysis of demographic and social changes in Klaipėda suburbs was carried out by D. Verkulevičiūtė-Kriekienė, I. Nomeikienė. P. Lakov, I. Shopova presented opportunities of cultural and historical attraction for tourists in Bulgaria. D. Behmane, D. Rutitis, V. Savicka rated the websites of health care providers. K. Casno, D. Šķiltere, B. Sloka, and G. Tauraitė-Janušauskienė discussed the role of social entrepreneurship in the context of sustainable development. The role of digitalization in the development of civil society is analyzed in the article by E. Lielpēters, while the online car rental wars are discussed in S. H. Pramudya’s article. E. Dundure, B. Sloka’s article analyzes the Latvian pension system, while the problems of material deprivation are analyzed in B. Sloka, K.Cipane’s article. The effect of fear of loss was discussed by V. Tauraitė. The importance of the use of emotional intelligence in vocational training was studied by A. Lice, B. Sloka. A review of H. Hilmarson’s book written by S. Kumar can also be found in this issue. Enjoy your readings.