This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical background. The first part contains a presentation of the arbitrage theory in discrete time. In the second part, the theories of stochastic calculus and parabolic PDEs are developed in detail and the classical arbitrage theory is analyzed in a Markovian setting by means of of PDEs techniques. After the martingale representation theorems and the Girsanov theory have been presented, arbitrage pricing is...
This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is des...
This book explores several aspects of fractional Brownian motion, including the stochastic integration, the study of its supremum and its appearance as limit of partial sums involving stationary sequences.
This book explores several aspects of fractional Brownian motion, including the stochastic integration, the study of its supremum and its appearance a...
This research monograph provides an introduction to tractable multidimensional diffusion models, where transition densities, Laplace transforms, Fourier transforms, fundamental solutions or functionals can be obtained in explicit form.The book also provides an introduction to the use of Lie symmetry group methods for diffusions, which allows to compute a wide range of functionals. Besides the well-known methodology on affine diffusions it presents a novel approach to affine processes with applications in finance.Numerical methods, including Monte Carlo and quadrature methods, are discussed...
This research monograph provides an introduction to tractable multidimensional diffusion models, where transition densities, Laplace transforms, Fouri...
This book gives an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes and it considers some related diffusions such as Wright-Fisher processes. It focuses on different simulation schemes for these processes, especially second-order schemes for the weak error. It also presents some models, mostly in the field of finance, where these methods are relevant and provides some numerical experiments.
The book explains the mathematical background to understand affine diffusions and analyze the accuracy of the schemes.
This book gives an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes and it considers some related diffusions s...
Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years due mainly to the impetus of the authors and their collaborators a powerful connection has been established between stochastic geometry and the...
Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, ti...
This book explores several aspects of fractional Brownian motion, including the stochastic integration, the study of its supremum and its appearance as limit of partial sums involving stationary sequences.
This book explores several aspects of fractional Brownian motion, including the stochastic integration, the study of its supremum and its appearance a...
This book gives an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes and it considers some related diffusions such as Wright-Fisher processes. It focuses on different simulation schemes for these processes, especially second-order schemes for the weak error. It also presents some models, mostly in the field of finance, where these methods are relevant and provides some numerical experiments.
The book explains the mathematical background to understand affine diffusions and analyze the accuracy of the schemes.
This book gives an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes and it considers some related diffusions s...
This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion.
This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. In particular, models of ...
