Optimal stopping problems in mathematical finance

This thesis is concerned with the pricing of American-type contingent claims. First, the explicit solutions to the perpetual American compound option pricing problems in the Black-Merton-Scholes model for financial markets are presented. Compound options are financial contracts which give their holders the right (but not the obligation) to buy or sell some other options at certain times in the future by the strike prices given. The method of proof is based on the reduction of the initial two-step optimal stopping problems for the underlying geometric Brownian motion to appropriate sequences of ordinary one-step problems. The latter are solved through their associated one-sided free-boundary problems and the subsequent martingale verification for ordinary differential operators. The closed form solution to the perpetual American chooser option pricing problem is also obtained, by means of the analysis of the equivalent two-sided free-boundary problem. Second, an extension of the Black-Merton-Scholes model with piecewise-constant dividend and volatility rates is considered. The optimal stopping problems related to the pricing of the perpetual American standard put and call options are solved in closed form. The method of proof is based on the reduction of the initial optimal stopping problems to the associated free-boundary problems and the subsequent martingale verification using a local time-space formula. As a result, the explicit algorithms determining the constant hitting thresholds for the underlying asset price process, which provide the optimal exercise boundaries for the options, are presented. Third, the optimal stopping games associated with perpetual convertible bonds in an extension of the Black-Merton-Scholes model with random dividends under different information flows are studied. In this type of contracts, the writers have a right to withdraw the bonds before the holders can exercise them, by converting the bonds into assets. The value functions and the stopping boundaries' expressions are derived in closed-form in the case of observable dividend rate policy, which is modelled by a continuous-time Markov chain. The analysis of the associated parabolic-type free-boundary problem, in the case of unobservable dividend rate policy, is also presented and the optimal exercise times are proved to be the first times at which the asset price process hits boundaries depending on the running state of the filtering dividend rate estimate. Moreover, the explicit estimates for the value function and the optimal exercise boundaries, in the case in which the dividend rate is observable by the writers but unobservable by the holders of the bonds, are presented. Finally, the optimal stopping problems related to the pricing of perpetual American options in an extension of the Black-Merton-Scholes model, in which the dividend and volatility rates of the underlying risky asset depend on the running values of its maximum and its maximum drawdown, are studied. The latter process represents the difference between the running maximum and the current asset value. The optimal stopping times for exercising are shown to be the first times, at which the price of the underlying asset exits some regions restricted by certain boundaries depending on the running values of the associated maximum and maximum drawdown processes. The closed-form solutions to the equivalent free-boundary problems for the value functions are obtained with smooth fit at the optimal stopping boundaries and normal reflection at the edges of the state space of the resulting three-dimensional Markov process. The optimal exercise boundaries of the perpetual American call, put and strangle options are obtained as solutions of arithmetic equations and first-order nonlinear ordinary differential equations

Optimal stopping problems in diffusion-type models with running maxima and drawdowns

We study optimal stopping problems related to the pricing of perpetual American options in an extension of the Black-Merton-Scholes model in which the dividend and volatility rates of the underlying risky asset depend on the running values of its maximum and maximum drawdown. The optimal stopping times of exercise are shown to be the first times at which the price of the underlying asset exits some regions restricted by certain boundaries depending on the running values of the associated maximum and maximum drawdown processes. We obtain closed-form solutions to the equivalent free-boundary problems for the value functions with smooth fit at the optimal stopping boundaries and normal reflection at the edges of the state space of the resulting three-dimensional Markov process. We derive first-order nonlinear ordinary differential equations for the optimal exercise boundaries of the perpetual American standard options

The 7 steps to support teaching, learning and research from Digital Libraries

Libraries are well-positioned in order to work in cross-disciplinary teams in teaching and learning as well as in research landscape. The new trends and significant challenges in education and the important developments in technology are drivers for developing and changing libraries. For instance, among others, the economic and political pressures, the evolving nature of the scholarly record and the research data management areexamples of areas that are affected by this change. The seven steps described in the following pages were selected by the authors after a thorough bibliography review, the application of previous professional knowledge and experience within the field of libraries and further discussion of the topic. These steps are intended to be a roadmap to accelerate the transformation of digital libraries aiming to support teaching, learning and research.Las bibliotecas están bien posicionadas para trabajar en equipos interdisciplinarios en la enseñanza y el aprendizaje, así como en el campo de la investigación. Las nuevas tendencias y retos importantes en la educación y los importantes desarrollos tecnológicos son motores para el desarrollo y el cambio de las bibliotecas. Por ejemplo, entre otras, las presiones económicas y políticas, la naturaleza evolutiva del registro académico y la gestión de datos de investigación son ejemplos de áreas que se ven afectadas por este cambio. Se seleccionaron los siete pasos descritos en las siguientes páginas. Los autores después de una exhaustiva revisión bibliográfica, aplicación de los conocimientos y experiencias profesionales anteriores dentro del campo de las bibliotecas y una mayor discusión del tema. Estos pasos están destinados a ser una hoja de ruta para acelerar la transformación de bibliotecas digitales con el objetivo de apoyar la enseñanza, aprendizaje e investigación.Les biblioteques estan ben posicionades per a treballar en equips interdisciplinaris en l'ensenyament i l'aprenentatge, així com en el camp de la recerca. Les noves tendències i reptes importants en l'educació i els importants desenvolupaments tecnològics són motors per al desenvolupament i el canvi de les biblioteques. Per exemple, entre unes altres, les pressions econòmiques i polítiques, la naturalesa evolutiva del registre acadèmic i la gestió de dades de recerca són exemples d'àrees que es veuen afectades per aquest canvi. Es van seleccionar els set passos descrits en les següents pàgines. Els autors després d'una exhaustiva revisió bibliogràfica, aplicació dels coneixements i experiències professionals anteriors dins del camp de les biblioteques i una major discussió del tema. Aquests passos estan destinats a ser un full de ruta per a accelerar la transformació de biblioteques digitals amb l'objectiu de recolzar l'ensenyament, aprenentatge i recerca

Gathering Background Knowledge for Story Understanding through Crowdsourcing

Successfully comprehending stories involves integration of the story information with the reader\u27s own background knowledge. A prerequisite, then, of building automated story understanding systems is the availability of such background knowledge. We take the approach that knowledge appropriate for story understanding can be gathered by sourcing the task to the crowd. Our methodology centers on breaking this task into a sequence of more specific tasks, so that human participants not only identify relevant knowledge, but also convert it into a machine-readable form, generalize it, and evaluate its appropriateness. These individual tasks are presented to human participants as missions in an online game, offering them, in this manner, an incentive for their participation. We report on an initial deployment of the game, and discuss our ongoing work for integrating the knowledge gathering task into a full-fledged story understanding engine

On the drawdowns and drawups in diffusion-type models with running maxima and minima

We obtain closed-form expressions for the values of joint Laplace transforms of the running maximum and minimum of a diffusion-type process stopped at the first time at which the associated drawdown and drawup processes hit constant levels. It is assumed that the coefficients of the diffusion-type process are regular functions of the running values of the process itself, its maximum and minimum, as well as its maximum drawdown and maximum drawup processes. The proof is based on the solution to the equivalent boundary-value problems and application of the normal-reflection conditions for the value functions at the edges of the state space of the resulting five-dimensional Markov process. We show that the joint Laplace transforms represent linear combinations of solutions to the systems of first-order partial differential equations arising from the application of the normal-reflection conditions

Land and capital accumulation in Greek agriculture by region (1950-2010)

After the liberation (1828) the land that belonged to the Turks became state-owned land. A large part of the state’s revenue was covered by the rent. The distribution of national domain, as it was called; in the year 1871 solved the problem that arose by the farmer’s discomfort against the state-landlord. A new important issue arose by the adaptation of Thessaly (1881), where the Turks when they were leaving, sold their land, often for very low price, to Greek capitalists. Thus, the manors appeared. This issue took tremendous dimensions at the beginning of the 20th century with the villagers’ riots at this region. After the Balkan Wars (1912, 1913) and World War I the annexation of Macedonia, Epirus and Thrace, where domains prevailed, inflated the problem. The entrance of the refugees after the Asia Minor disaster (1922) led the governments to extended land consolidation. In order to multiply the farming lands, at the decade of 1930, large productive works were carried out in northern Greece (drainage of lakes, ponds etc.). After World War II the program of landimprovement works was accelerated and as a result the number of irrigated lands was significantly increased and the cultivated land differed, while the plantations expanded very quickly. During 1950 to 80 through subsidy loans by the public Agriculture Bank, a modernization of agriculture was attempted (mechanization, improved seeds, pesticides etc) and restructuring of farming was partially achieved. The aim of this paper hereof is double: Firstly, it seeks to investigate, something which does not exist in Greek bibliography, what was the value of the land, in relevance to the capital accumulation, not only in the whole country, but also per prefecture and secondly, which was the contribution of the land improvement at the growth of the product. The data arose from long-term investigation of authors over the subject of framing the agriculture economy sizes and the method was based on the archives consultation.peer-reviewe

DEVELOPING AN ACADEMIC INSTITUTIONAL REPOSITORY. THE CASE OF THE OPEN UNIVERSITY OF CYPRUS

The amount of digital content produced nowadays, is enormous. Academic institutions produce and make available a plethora of digital objects like research articles, theses, dissertations, reports, audiovisual collections and many others. In addition, academic libraries digitize materials to create collections of historical, political and scientific significance and are responsible for keeping, preserving, archiving and publishing the content produced by their students and academic personnel. Aiming in that direction, the Open University of Cyprus, an institution responsible for delivering distance learning at the Republic of Cyprus, designed and deployed “Kypseli” Institutional Repository. In this work, the authors depict the methodology and tools used for building an academic institutional repository using open source tools at the Open University of Cyprus. Moreover, the procedures used for publishing content and the integration of the repository to the rest of the university’s infrastructure are analysed, along with the challenges faced during the implementation and deployment phase. In addition, a number of metrics are presented, accompanied by statistics of usage

Watermark options

We consider a new family of derivatives whose payoffs become strictly positive when the price of their underlying asset falls relative to its historical maximum. We derive the solution to the discretionary stopping problems arising in the context of pricing their perpetual American versions by means of an explicit construction of their value functions. In particular, we fully characterise the free-boundary functions that provide the optimal stopping times of these genuinely two-dimensional problems as the unique solutions to highly non-linear first order ODEs that have the characteristics of a separatrix. The asymptotic growth of these free-boundary functions can take qualitatively different forms depending on parameter values, which is an interesting new feature