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| Author | : Tomas Björk |
| Publisher | : Cambridge University Press |
| Total Pages | : 323 |
| Release | : 2021-06-17 |
| Genre | : Business & Economics |
| ISBN | : 1316518671 |
Develop a deep understanding and working knowledge of point-process theory as well as its applications in finance.
| Author | : Tomas Björk |
| Publisher | : Cambridge University Press |
| Total Pages | : 324 |
| Release | : 2021-06-17 |
| Genre | : Mathematics |
| ISBN | : 1009008447 |
The theory of marked point processes on the real line is of great and increasing importance in areas such as insurance mathematics, queuing theory and financial economics. However, the theory is often viewed as technically and conceptually difficult and has proved to be a block for PhD students looking to enter the area. This book gives an intuitive picture of the central concepts as well as the deeper results, while presenting the mathematical theory in a rigorous fashion and discussing applications in filtering theory and financial economics. Consequently, readers will get a deep understanding of the theory and how to use it. A number of exercises of differing levels of difficulty are included, providing opportunities to put new ideas into practice. Graduate students in mathematics, finance and economics will gain a good working knowledge of point-process theory, allowing them to progress to independent research.
| Author | : Peter Tankov |
| Publisher | : CRC Press |
| Total Pages | : 552 |
| Release | : 2003-12-30 |
| Genre | : Business & Economics |
| ISBN | : 1135437947 |
WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic
| Author | : D.J. Daley |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 590 |
| Release | : 2007-11-12 |
| Genre | : Mathematics |
| ISBN | : 0387213376 |
This is the second volume of the reworked second edition of a key work on Point Process Theory. Fully revised and updated by the authors who have reworked their 1988 first edition, it brings together the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition: limit theorems, ergodic theory, Palm theory, and evolutionary behaviour via martingales and conditional intensity. The very substantial new material in this second volume includes expanded discussions of marked point processes, convergence to equilibrium, and the structure of spatial point processes.
| Author | : Kay Giesecke |
| Publisher | : |
| Total Pages | : 9 |
| Release | : 2009 |
| Genre | : |
| ISBN | : |
Point processes with stochastic intensities are ubiquitous in many application areas, including finance, insurance, reliability and queuing. They can be simulated from standard Poisson arrivals by time-scaling with the cumulative intensity, whose path is typically generated with a discretization method. However, discretization introduces bias into the simulation results. This paper proposes a method for the exact simulation of point processes with stochastic intensities. The method leads to unbiased estimators. It is illustrated for a point process whose intensity follows an affine jump-diffusion process.
| Author | : Bernt Øksendal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 263 |
| Release | : 2007-04-26 |
| Genre | : Mathematics |
| ISBN | : 3540698264 |
Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.
| Author | : Floyd B. Hanson |
| Publisher | : SIAM |
| Total Pages | : 461 |
| Release | : 2007-11-22 |
| Genre | : Mathematics |
| ISBN | : 0898716330 |
A practical, entry-level text integrating the basic principles of applied mathematics and probability, and computational science.
| Author | : Floyd B. Hanson |
| Publisher | : SIAM |
| Total Pages | : 472 |
| Release | : 2007-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898718638 |
This self-contained, practical, entry-level text integrates the basic principles of applied mathematics, applied probability, and computational science for a clear presentation of stochastic processes and control for jump diffusions in continuous time. The author covers the important problem of controlling these systems and, through the use of a jump calculus construction, discusses the strong role of discontinuous and nonsmooth properties versus random properties in stochastic systems.
| Author | : Anca Patricia Vacarescu |
| Publisher | : Stanford University |
| Total Pages | : 192 |
| Release | : 2011 |
| Genre | : |
| ISBN | : |
We consider the nonlinear filtering problem for partially observed Generalized Hawkes Processes, which can be applied in the context of portfolio credit risk. The problem belongs to the larger class of hidden Markov models, where the counting process is observed at discrete points in time and the observations are sparse, while the intensity driving process in unobservable. We construct the conditional distribution of the process given the information filtration and we discuss the analytical and numerical properties of the corresponding filters. In particular, we study the sensitivity of the filters with respect to the parameters of the model, and we obtain a monotonicity result with respect to the jump and the volatility terms driving the intensity. Using the scaled process, we provide necessary and sufficient conditions for the frequency of time observations in terms of the parameters of the model, to ensure a good performance of the filter. We also address the problem of parameter estimation for the Generalized Hawkes Process in the framework of the EM algorithm, and we analyze the effect of the self-exciting feature of our process on the asymptotic and numerical properties of the estimators.
| Author | : S.T Rachev |
| Publisher | : Elsevier |
| Total Pages | : 707 |
| Release | : 2003-03-05 |
| Genre | : Business & Economics |
| ISBN | : 0080557732 |
The Handbooks in Finance are intended to be a definitive source for comprehensive and accessible information in the field of finance. Each individual volume in the series should present an accurate self-contained survey of a sub-field of finance, suitable for use by finance and economics professors and lecturers, professional researchers, graduate students and as a teaching supplement. The goal is to have a broad group of outstanding volumes in various areas of finance. The Handbook of Heavy Tailed Distributions in Finance is the first handbook to be published in this series. This volume presents current research focusing on heavy tailed distributions in finance. The contributions cover methodological issues, i.e., probabilistic, statistical and econometric modelling under non- Gaussian assumptions, as well as the applications of the stable and other non -Gaussian models in finance and risk management.
