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Stochastic Finance
Mathematics, as the language of science, has always played a role in the development of knowledge and technology. Presently, the high-tech character of modern business has increased the need for advanced methods, which rely to a large extent on mathematical techniques. It has become essential for the financial analyst to possess a high degree of proficiency in these mathematical techniques. The essays in Stochastic Finance describe many of these techniques.
Stochastic Calculus for Fractional Brownian Motion and Applications
Fractional Brownian motion (fBm) has been widely used to model a number of phenomena in diverse fields from biology to finance. This huge range of potential applications makes fBm an interesting object of study. fBm represents a natural one-parameter extension of classical Brownian motion therefore it is natural to ask if a stochastic calculus for fBm can be developed. This is not obvious, since fBm is neither a semimartingale (except when H = ½), nor a Markov process so the classical mathematical machineries for stochastic calculus are not available in the fBm case.
Parameter Estimation in Stochastic Differential Equations
Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modelling complex phenomena and making beautiful decisions. The subject has attracted researchers from several areas of mathematics and other related fields like economics and finance. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods. Useful because of the current availability of high frequency data is the study of refined asymptotic properties of several estimators when the observation time length is large and the observation time interval is small. Also space time white noise driven models, useful for spatial data, and more sophisticated non-Markovian and non-semimartingale models like fractional diffusions that model the long memory phenomena are examined in this volume.
In Memoriam Paul-André Meyer - Séminaire de Probabilités XXXIX
The 39th volume of Séminaire de Probabilités is a tribute to the memory of Paul André Meyer. His life and achievements are recalled in this book, and tributes are paid by his friends and colleagues. This volume also contains mathematical contributions to classical and quantum stochastic calculus, the theory of processes, martingales and their applications to mathematical finance and Brownian motion. These contributions provide an overview on the current trends of stochastic calculus.
From Stochastic Calculus to Mathematical Finance : The Shiryaev Festschrift
The Festschrift is a collection of papers, including several surveys, written by his former students, co-authors and colleagues. These reflect the wide range of scientific interests of the teacher and his Moscow school. The topics range from the disorder problems to stochastic calculus and their applications to mathematical economics and finance. A full biobibliography of Shiryaev's works is included. The book represents the modern state of art of many aspects of a quickly maturing theory and will be an essential source and reading for researchers in this area.
