Compound Lévy random bridges and credit risky asset pricing

In this thesis, we study random bridges of a certain class of Lévy processes and their applications to credit risky asset pricing. In the first part, we construct the compound random bridges(CLRBs) and analyze some tools and properties that make them suitable models for information processes. We focus on the Markov property, dynamic consistency, measure changes and increment distributions. Thereafter, we consider applications in credit risky asset pricing. We generalize the information based credit risky asset pricing framework to incorporate prematurity default possibilities. Lastly we derive closed-form expressions for default trends and intensities for credit risky bonds with CLRB as the background partial information process. We obtain analytical expressions for specific CLRBs. The second part looks at application of stochastic filtering in the current information based asset pricing framework. First, we formulate credit risky asset pricing in the information-based framework as a filtering problem under incomplete information. We derive the Kalman-Bucy filter in one dimension for bridges of Lévy processes with a given finite variance

Stochastic Transport in Upper Ocean Dynamics

This open access proceedings volume brings selected, peer-reviewed contributions presented at the Stochastic Transport in Upper Ocean Dynamics (STUOD) 2021 Workshop, held virtually and in person at the Imperial College London, UK, September 20–23, 2021. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography

Stochastic Transport in Upper Ocean Dynamics

This open access proceedings volume brings selected, peer-reviewed contributions presented at the Stochastic Transport in Upper Ocean Dynamics (STUOD) 2021 Workshop, held virtually and in person at the Imperial College London, UK, September 20–23, 2021. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography

Pricing Energy, Weather and Emission Derivatives under Future Information

The aim of this thesis mainly consists in the computation of risk-neutral option prices for energy, weather, emission and commodity derivatives, whereas we innovatively take future information – which we assume to be available to well-informed market insiders – into account via several customized enlargements of the underlying information filtrations. In this regard, we inter alia derive European as well as exotic option price formulas for electricity derivatives such as traded at the European Energy Exchange EEX, for example, but yet under the incorporation of forward-looking information about possible future electricity spot price behavior. Furthermore, we provide both utility-maximizing anticipating portfolio selection procedures and optimal liquidation strategies for electricity futures portfolios yielding minimal expected trading costs under forward-looking price impact considerations. Moreover, we correlate electricity spot prices with outdoor temperature and treat a related electricity derivatives pricing problem even under additional temperature forecasts. In this insider trading context, we also derive explicit expressions for different types of temperature futures indices such as usually traded at the Chicago Mercantile Exchange CME, for instance, and provide various pricing formulas for options written on the latter. Additionally, we construct optimal positions in a temperature futures portfolio under forecasted weather information in order to hedge against both temporal and spatial temperature risk adequately. Further on, we treat the pricing of carbon emission allowances, such as commonly traded in the European Union Emission Trading Scheme EU ETS, but under supplementary insider information on the future market zone net position. In this context, we propose two improved arithmetic multi-state approaches to model the ‘length of the market net position’ more realistically than in existing models. By the way, throughout this work we frequently discuss customized martingale compensators under enlarged filtrations and related information premia associated to our specific insider trading frameworks. Finally, we invent nonlinear double-jump stochastic filtering techniques for generalized Lévy-type processes in order to (theoretically) calibrate the emerging incomplete market models

Stability Problems for Stochastic Models: Theory and Applications II

Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21­25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: Limit theorems and stability problems; Asymptotic theory of stochastic processes; Stable distributions and processes; Asymptotic statistics; Discrete probability models; Characterization of probability distributions; Insurance and financial mathematics; Applied statistics; Queueing theory; and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described