Synopses & Reviews
This book highlights recent developments in mathematical control theory and its applications to finance. It presents a collection of original contributions by distinguished scholars, addressing a large spectrum of problems and techniques. Control theory provides a large set of theoretical and computational tools with applications in a wide range of fields, ranging from "pure" areas of mathematics up to applied sciences like finance. Stochastic optimal control is a well established and important tool of mathematical finance. Other branches of control theory have found comparatively less applications to financial problems, but the exchange of ideas and methods has intensified in recent years. This volume should contribute to establish bridges between these separate fields. The diversity of topics covered as well as the large array of techniques and ideas brought in to obtain the results make this volume a valuable resource for advanced students and researchers.
Table of Contents
Extremals Flows and Infinite Horizon Optimization.- Laplace Transforms and the American Call Option.- Time Change, Volatility, and Turbulence.- External Dynamical Equivalence of Analytic Control Systems.- On Option-Valuation in Illiquid Markets: Invariant Solutions to a Nonlinear Model.- Predicting the Time of the Ultimate Maximum for Brownian Motion with Drift.- A Stochastic Demand Model for Optimal Pricing of Non-Life Insurance Policies.- Optimality of Deterministic Policies for Certain Stochastic Control Problems with Multiple Criteria and Constraints.- Higher-Order Calculus of Variations on Time Scales.- Finding Invariants of Group Actions oon Function Spaces, a General Methodology from Non-Abelian Harmonic Analysis.- Nonholonomic Interpolation for Kinematic Problems, Entropy and Complexity.- Instalment Options: A Closed-Form Solution and the Limiting Case.- Existence and Lipschitzian Regularity for Relaxed Minimizers.- Pricing of Defaultable Securities under Stochastic Interest.- Spline Cubatures for Expectations of Diffusion Processes and Optimal Stopping in Higher Dimensions (with Computational Finance in View).- An Approximate Solution for Optimal Portfolio in Incomplete Markets.- Carleman Linearization of Linearly Observable Polynomial Systems.- Observability of Nonlinear Control Systems on Time Scales - Sufficient Conditions.- Sufficient Optimality Conditions for a Bang-bang Trajectory in a Bolza Problem.- Modelling Energy Markets with Extreme Spikes.- Generalized Bayesian Nonlinear Quickest Detection Problems: On Markov Family of Sufficient Statistics.- Necessary Optimality Condition for a Discrete Dead Oil Isotherm Optimal Control Problem.- Managing Operational Risk: Methodology and Prospects.