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

Managing COVID- 19 Pandemic Crisis: The Case of Greece

This qualitative study analyzes the Greek government’s crisis management practice and public communication efforts during two waves of the COVID-19 pandemic in 2020. Integrating both crisis management theories and the World Health Organization’s pandemic control plans, discourse analysis and case study approaches were taken to analyze how Greek’s key government and public health authorities communicated with the public using different frames and crisis response strategies. Evaluations were conducted to assess the Greek government’s crisis communication procedures and the effectiveness of different rhetorical strategies used as evidenced in public briefings and public speeches

Perception of Reverberation in Domestic and Automotive Environments

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Image Restoration Strategies for the (mis-) handling of COVID – 19 Pandemic in Greece

During the COVID-19 pandemic outbreak all countries around the world used several kinds of response strategies to protect public health and control the outbreak. The main aim was to stop the disease from spreading into the community and put a pressure on the health system of the countries. However, severe measures like lockdown of cities and countries brought side-crises like economic pressure on the individuals, corporations and even the state itself. Although the Greek Government was considered to have managed the first phase of the crisis in March effectively, during the aftermath of the first phase, the complete opening of the economy and tourism, the lowering of measures leaded to the increase of new cases. The increased number of cases together with the late imposition of a new lockdown, leaded to the perception of a governmental failure. This perception mobilized direct or indirect image restoration strategies by officials of the Greek Government to maintain the positive image of their handling despite the general perceptions. This paper explores the image restoration strategies used by the prime minister of Greece for the handlings of the second phase of the pandemic in Greece. The methodology used is discourse analysis with the tools of Image Restoration Strategies by Benoit (1995) from October till December 2020

Διερεύνηση κριτηρίων χωροθέτησης και περιβαλλοντικών επιπτώσεων από την κατασκευή αγωγού φυσικού αερίου υψηλής πίεσης από την Κόρινθο (Εξαμίλια) έως την ΒΙ.ΠΕ. Πατρών

Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Γεωπληροφορική

A New Look at Ghost Normalization

Batch normalization (BatchNorm) is an effective yet poorly understood technique for neural network optimization. It is often assumed that the degradation in BatchNorm performance to smaller batch sizes stems from it having to estimate layer statistics using smaller sample sizes. However, recently, Ghost normalization (GhostNorm), a variant of BatchNorm that explicitly uses smaller sample sizes for normalization, has been shown to improve upon BatchNorm in some datasets. Our contributions are: (i) we uncover a source of regularization that is unique to GhostNorm, and not simply an extension from BatchNorm, (ii) three types of GhostNorm implementations are described, two of which employ BatchNorm as the underlying normalization technique, (iii) by visualising the loss landscape of GhostNorm, we observe that GhostNorm consistently decreases the smoothness when compared to BatchNorm, (iv) we introduce Sequential Normalization (SeqNorm), and report superior performance over state-of-the-art methodologies on both CIFAR--10 and CIFAR--100 datasets

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