Między Rosją a Czechosłowacją: Ruś łemkowska w polityce międzynarodowej w dobie starań o podmiotowość polityczną, 1918-1921

Between Russia and Czechoslovakia: Lemko Rus’ Struggle for Political Independence in the Years 1918-1921 and International PoliticsThe events in Lemko Rus had, in the years 1918-1921, a subjective and political character, and were the result of Lemkos’ own initiatives and activities, and not just external influences. They proved to be the national maturation of the Lemko community. However, it cannot be said that the newly created Lemko councils aimed at or constituted their own Lemko state with the headquarters in the village of Florynka. It becomes clear after analysing the chronology of Lemko political postulates in the context of events in the regional and global plane. None of the subsequent stages of the process of specifying their nationality by the Lemkos was connected with the idea of a separate Lemko statehood. Formally speaking, i.e., from the perspective of law and international relations, the Lemko region first wanted to belong to the Russian state, then to Czechoslovakia, always strongly rejecting the notion of being part of the resurgent Poland and the then-created Ukraine. Czechoslovakia was not an alternative to Russia for Lemko politicians, but only a tactical necessity against the momentary, as it was believed, impossibility to implement the original Russian option. It was a case created by a coincidence of ad-hoc circumstances. Be the Lemkos’ own country in the national sense, that is, they met both the political and cultural criteria of belonging there, which were important to their community. The Czechoslovak option somehow forced, or rather made possible the second option – striving to create a local state with a wider formula than just the Lemko region, connecting all Rusyns living in Austria-Hungary, that is also those from Eastern Galicia, Bukovina and Hungary. Such a Carpatho-Ruthenian republic was supposed to be a substitute, necessary for formal reasons, as an autonomous element in the federal structure of the Czechoslovak state, and for political reasons, as a safeguard for the national aspirations of the such a Carpatho-Rusyn and a guarantee of their future unification with democratic Russia. While Russia, both tsarist and liberal, guided by its national doctrine, was willing to unconditionally include all Austro-Hungarian Ruthenians in its borders, including also westernmost Lemkos, Czechoslovak leaders wanted to bite only as much as they could chew economically and politically, i.e. – include only regions rich in cities or natural deposits. The poor and non-urbanized Lemko region was treated only as a convenient item in their subversive game of borders with Poland.

Pricings and hedgings of the perpetual Russian options

In this paper, we study the optimal stopping time and the optimal stopping boundary for the perpetual Russian option under the diffusion process. The general continuation region is characterized by a function b(p,t) depending on both variables t and the maximum value of the stock and initial starting value P0. Previous studies assume that the continuation region is given by a function depending upon the time t only. This is unreal hypothesis for the diffusion to achieve. Our result shows that the perpetual Russian option can be described by a Black–Scholes equation over the continuation region and smooth boundary conditions on the optimal stopping boundary. Furthermore, we develop an evaluation method from the lookback option on a stopping time, and establish the Greek letters for the perpetual Russian option. We obtain the exact upper bound for the prices of the perpetual Russian options and demonstrate that both the payoff and the optimal stopping time are path-dependent by Monte Carlo simulations.

THE VALUATION OF RUSSIAN OPTIONS FOR DOUBLE EXPONENTIAL JUMP DIFFUSION PROCESSES

In this paper, we derive closed form solution for Russian option with jumps. First, we discuss the pricing of Russian options when the stock pays dividends continuously. Secondly, we derive the value function of Russian options by solving the ordinary differential equation with some conditions (the value function is continuous and differentiable at the optimal boundary for the buyer). And we investigate properties of optimal boundaries of the buyer. Finally, some numerical results are presented to demonstrate analytical properties of the value function.