Optimality and Risk - Modern Trends in Mathematical Finance : The Kabanov Festschrift

Problems of stochastic optimization and various mathematical aspects of risk are the main themes of this contributed volume. The readers learn about the recent results and techniques of optimal investment, risk measures and derivative pricing. There are also papers touching upon credit risk, martingale theory and limit theorems. Forefront researchers in probability and financial mathematics have contributed to this volume paying tribute to Yuri Kabanov, an eminent researcher in probability and mathematical finance, on the occasion of his 60 th birthday. The volume gives a fair overview of these topics and the current approaches. Front Matter....Pages I-XVIII On the Extension of the Namioka-Klee Theorem and on the Fatou Property for Risk Measures....Pages 1-28 On Certain Distributions Associated with the Range of Martingales....Pages 29-38 Differentiability Properties of Utility Functions....Pages 39-48 Exponential Utility Indifference Valuation in a General Semimartingale Model....Pages 49-86 The Expected Number of Intersections of a Four Valued Bounded Martingale with any Level May be Infinite....Pages 87-98 Immersion Property and Credit Risk Modelling....Pages 99-132 Optimal Consumption and Investment with Bounded Downside Risk for Power Utility Functions....Pages 133-170 On Comparison Theorem and its Applications to Finance....Pages 171-181 Examples of FCLT in Random Environment....Pages 183-196 The Optimal Time to Exchange one Asset for Another on Finite Interval....Pages 197-210 Arbitrage Under Transaction Costs Revisited....Pages 211-225 On the Linear and Nonlinear Generalized Bayesian Disorder Problem (Discrete Time Case)....Pages 227-236 Long Time Growth Optimal Portfolio with Transaction Costs....Pages 237-250 On the Approximation of Geometric Fractional Brownian Motion....Pages 251-266