From Stochastic Calculus to Mathematical Finance

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 Shiryaevs 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.

On Numerical Approximation of Stochastic Burgers' Equation.- Optimal Time to Invest under Tax Exemptions.- A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales.- Interplay between Distributional and Temporal Dependence. An Empirical Study with High-frequency Asset Returns.- Asymptotic Methods for Stability Analysis of Markov Dynamical Systems with Fast Variables.- Some Particular Problems of Martingale Theory.- On the Absolute Continuity and Singularity of Measures on Filtered Spaces: Separating Times.- Optimal Hedging with Basis Risk.- Moderate Deviation Principle for Ergodic Markov Chain. Lipschitz Summands.- Remarks on Risk Neutral and Risk Sensitive Portfolio Optimization.- On Existence and Uniqueness of Reflected Solutions of Stochastic Equations Driven by Symmetric Stable Processes.- A Note on Pricing, Duality and Symmetry for Two-Dimensional Lévy Markets.- Enlargement of Filtration and Additional Information in Pricing Models: BayesianApproach.- A Minimax Result for f-Divergences.- Impulse and Absolutely Continuous Ergodic Control of One-Dimensional Itô Diffusions.- A ConsumptionInvestment Problem with Production Possibilities.- Multiparameter Generalizations of the DalangMorton Willinger Theorem.- A Didactic Note on Affine Stochastic Volatility Models.- Uniform Optimal Transmission of Gaussian Messages.- A Note on the Brownian Motion.- Continuous Time Volatility Modelling: COGARCH versus OrnsteinUhlenbeck Models.- Tail Distributions of Supremum and Quadratic Variation of Local Martingales.- Stochastic Differential Equations: A Wiener Chaos Approach.- A Martingale Equation of Exponential Type.- On Local Martingale and its Supremum: Harmonic Functions and beyond.- On the Fundamental Solution of the KolmogorovShiryaev Equation.- Explicit Solution to an Irreversible Investment Model with a Stochastic Production Capacity.- Gittins Type Index Theorem for Randomly Evolving Graphs.- On the Existence of Optimal Portfolios for the Utility Maximization Problem in Discrete Time Financial Market Models.- The Optimal Stopping of a Markov Chain and Recursive Solution of Poisson and Bellman Equations.- On Lower Bounds for Mixing Coefficients of Markov Diffusions.