Contents
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
XII Contents
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 Itˆo 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
Contents XIII
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
Huyˆen 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