Dedicated to the eminent Russian mathematician Albert Shiryaev on the occasion of his 70th birthday, 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. The diversity of the topics and the comprehensive style of the papers make the book amenable and attractive for PhD students and young researchers.
Albert SHIRYAEV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XV
Publications of A.N. Shiryaev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XXI
On Numerical Approximation of Stochastic Burgers Equation
Aureli ALABERT, Istv´an GY ¨ ONGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Optimal Time to Invest under Tax Exemptions
Vadim I. ARKIN, Alexander D. SLASTNIKOV. . . . . . . . . . . . . . . . . . . . . . 17
A Central Limit Theorem for Realised Power and Bipower
Variations of Continuous Semimartingales
Ole E. BARNDORFF-NIELSEN, Svend Erik GRAVERSEN, Jean
JACOD, Mark PODOLSKIJ, Neil SHEPHARD . . . . . . . . . . . . . . . . . . . . . 33
Interplay between Distributional and Temporal Dependence.
An Empirical Study with High-frequency Asset Returns
Nick H. BINGHAM, Rafael SCHMIDT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Asymptotic Methods for Stability Analysis of Markov
Dynamical Systems with Fast Variables
Jevgenijs CARKOVS, Jordan STOYANOV. . . . . . . . . . . . . . . . . . . . . . . . . . 91
Some Particular Problems of Martingale Theory
Alexander CHERNY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
On the Absolute Continuity and Singularity of Measures
on Filtered Spaces: Separating Times
Alexander CHERNY, Mikhail URUSOV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Optimal Hedging with Basis Risk
Mark H.A. DAVIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Moderate Deviation Principle for Ergodic Markov Chain.
Lipschitz Summands
Bernard DELYON, Anatoly JUDITSKY, Robert LIPTSER . . . . . . . . . . . . 189
Remarks on Risk Neutral and Risk Sensitive Portfolio
Optimization
Giovanni B. DI MASI, 3Lukasz STETTNER . . . . . . . . . . . . . . . . . . . . . . . . 211
On Existence and Uniqueness of Reflected Solutions
of Stochastic Equations Driven by Symmetric Stable
Processes
Hans-J¨urgen ENGELBERT, Vladimir P. KURENOK, Adrian
ZALINESCU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
A Note on Pricing, Duality and Symmetry
for Two-Dimensional L´evy Markets
Jos´e FAJARDO, Ernesto MORDECKI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
Enlargement of Filtration and Additional Information
in Pricing Models: Bayesian Approach
Dario GASBARRA, Esko VALKEILA, Lioudmila VOSTRIKOVA . . . . . 257
A Minimax Result for f-Divergences
Alexander A. GUSHCHIN, Denis A. ZHDANOV . . . . . . . . . . . . . . . . . . . . 287
Impulse and Absolutely Continuous Ergodic Control
of One-Dimensional Ito Diffusions
Andrew JACK, Mihail ZERVOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
A Consumption-Investment Problem with Production
Possibilities
Yuri KABANOV, Masaaki KIJIMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
Multiparameter Generalizations of the Dalang-Morton-
Willinger Theorem
Yuri KABANOV, Yuliya MISHURA, Ludmila SAKHNO . . . . . . . . . . . 333
A Didactic Note on Affine Stochastic Volatility Models
Jan KALLSEN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
Uniform Optimal Transmission of Gaussian Messages
Pavel K. KATYSHEV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
A Note on the Brownian Motion
Kiyoshi KAWAZU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
Continuous Time Volatility Modelling: COGARCH versus
Ornstein-Uhlenbeck Models
Claudia KL ¨ UPPELBERG, Alexander LINDNER, Ross MALLER . . . . . . 393
Tail Distributions of Supremum and Quadratic Variation
of Local Martingales
Robert LIPTSER, Alexander NOVIKOV . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
Stochastic Differential Equations: A Wiener Chaos Approach
Sergey LOTOTSKY and Boris ROZOVSKII . . . . . . . . . . . . . . . . . . . . . . . . 433
A Martingale Equation of Exponential Type
Michael MANIA, Revaz TEVZADZE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507
On Local Martingale and its Supremum:
Harmonic Functions and beyond.
Jan OB3L ´ OJ, Marc YOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
On the Fundamental Solution of the Kolmogorov-Shiryaev
Equation
Goran PESKIR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
Explicit Solution to an Irreversible Investment Model
with a Stochastic Production Capacity
Huyen PHAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547
Gittins Type Index Theorem for Randomly Evolving Graphs
Ernst PRESMAN, Isaac SONIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567
On the Existence of Optimal Portfolios for the Utility
Maximization Problem in Discrete Time Financial Market
Models
Mikl´os R´ ASONYI, 3Lukasz STETTNER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589
The Optimal Stopping of a Markov Chain and Recursive
Solution of Poisson and Bellman Equations
Isaac M. SONIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609
On Lower Bounds for Mixing Coefficients of Markov
Diffusions
A.Yu. VERETENNIKOV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623
