Dedicated to the Russian mathematician Albert Shiryaev on his 70th birthday, this is a collection of papers written by his former students, co-authors and colleagues. The book represents the modern state of art of a quickly maturing theory and will be an essential source and reading for researchers in this area. Diversity of topics and comprehensive style of the papers make the book attractive for PhD students and young researchers.
Author(s): Yu. Kabanov, R. Lipster, J. Stoyanov
Edition: 1
Year: 2006
Language: English
Pages: 659
Contents......Page 10
Albert SHIRYAEV......Page 14
Publications of A.N. Shiryaev......Page 20
On Numerical Approximation of Stochastic Burgers' Equation......Page 37
Optimal Time to Invest under Tax Exemptions......Page 52
A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales......Page 68
Interplay between Distributional and Temporal Dependence. An Empirical Study with High-frequency Asset Returns......Page 104
Asymptotic Methods for Stability Analysis of Markov Dynamical Systems with Fast Variables......Page 126
Some Particular Problems of Martingale Theory......Page 144
On the Absolute Continuity and Singularity of Measures on Filtered Spaces: Separating Times......Page 160
Optimal Hedging with Basis Risk......Page 204
Moderate Deviation Principle for Ergodic Markov Chain. Lipschitz Summands......Page 223
Remarks on Risk Neutral and Risk Sensitive Portfolio Optimization......Page 244
On Existence and Uniqueness of Reflected Solutions of Stochastic Equations Driven by Symmetric Stable Processes......Page 260
A Note on Pricing, Duality and Symmetry for Two-Dimensional Lévy Markets......Page 282
Enlargement of Filtration and Additional Information in Pricing Models: Bayesian Approach......Page 290
A Minimax Result for f-Divergences......Page 319
Impulse and Absolutely Continuous Ergodic Control of One-Dimensional Itô Diffusions......Page 327
A Consumption-Investment Problem with Production Possibilities......Page 347
Multiparameter Generalizations of the Dalang-Morton-Willinger Theorem......Page 365
A Didactic Note on Affine Stochastic Volatility Models......Page 374
Uniform Optimal Transmission of Gaussian Messages......Page 400
A Note on the Brownian Motion......Page 415
Continuous Time Volatility Modelling: COGARCH versus Ornstein-Uhlenbeck Models......Page 423
Tail Distributions of Supremum and Quadratic Variation of Local Martingales......Page 450
Stochastic Differential Equations: A Wiener Chaos Approach......Page 462
A Martingale Equation of Exponential Type......Page 536
On Local Martingale and its Supremum: Harmonic Functions and beyond.......Page 546
On the Fundamental Solution of the Kolmogorov-Shiryaev Equation......Page 563
Explicit Solution to an Irreversible Investment Model with a Stochastic Production Capacity......Page 575
Gittins Type Index Theorem for Randomly Evolving Graphs......Page 594
On the Existence of Optimal Portfolios for the Utility Maximization Problem in Discrete Time Financial Market Models......Page 616
The Optimal Stopping of a Markov Chain and Recursive Solution of Poisson and Bellman Equations......Page 636
On Lower Bounds for Mixing Coefficients of Markov Diffusions......Page 649
