From Stochastic Calculus to Mathematical Finance: The Shiryaev Festschrift

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