Ebook: Mathematical Control Theory and Finance

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.

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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.

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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.
Content:
Front Matter....Pages I-XIII
Extremals Flows and Infinite Horizon Optimization....Pages 1-13
Laplace Transforms and the American Call Option....Pages 15-27
Time Change, Volatility, and Turbulence....Pages 29-53
External Dynamical Equivalence of Analytic Control Systems....Pages 55-69
On Option-Valuation in Illiquid Markets: Invariant Solutions to a Nonlinear Model....Pages 71-94
Predicting the Time of the Ultimate Maximum for Brownian Motion with Drift....Pages 95-112
A Stochastic Demand Model for Optimal Pricing of Non-Life Insurance Policies....Pages 113-136
Optimality of Deterministic Policies for Certain Stochastic Control Problems with Multiple Criteria and Constraints....Pages 137-148
Higher-Order Calculus of Variations on Time Scales....Pages 149-159
Finding Invariants of Group Actions on Function Spaces, a General Methodology from Non-Abelian Harmonic Analysis....Pages 161-186
Nonholonomic Interpolation for Kinematic Problems, Entropy and Complexity....Pages 187-210
Instalment Options: A Closed-Form Solution and the Limiting Case....Pages 211-229
Existence and Lipschitzian Regularity for Relaxed Minimizers....Pages 231-250
Pricing of Defaultable Securities under Stochastic Interest....Pages 251-263
Spline Cubatures for Expectations of Diffusion Processes and Optimal Stopping in Higher Dimensions (with Computational Finance in View)....Pages 265-291
An Approximate Solution for Optimal Portfolio in Incomplete Markets....Pages 293-310
Carleman Linearization of Linearly Observable Polynomial Systems....Pages 311-323
Observability of Nonlinear Control Systems on Time Scales - Sufficient Conditions....Pages 325-335
Sufficient Optimality Conditions for a Bang-bang Trajectory in a Bolza Problem....Pages 337-357
Modelling Energy Markets with Extreme Spikes....Pages 359-375
Generalized Bayesian Nonlinear Quickest Detection Problems: On Markov Family of Sufficient Statistics....Pages 377-386
Necessary Optimality Condition for a Discrete Dead Oil Isotherm Optimal Control Problem....Pages 387-395
Managing Operational Risk: Methodology and Prospects....Pages 397-417
Back Matter....Pages 419-420

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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.
Content:
Front Matter....Pages I-XIII
Extremals Flows and Infinite Horizon Optimization....Pages 1-13
Laplace Transforms and the American Call Option....Pages 15-27
Time Change, Volatility, and Turbulence....Pages 29-53
External Dynamical Equivalence of Analytic Control Systems....Pages 55-69
On Option-Valuation in Illiquid Markets: Invariant Solutions to a Nonlinear Model....Pages 71-94
Predicting the Time of the Ultimate Maximum for Brownian Motion with Drift....Pages 95-112
A Stochastic Demand Model for Optimal Pricing of Non-Life Insurance Policies....Pages 113-136
Optimality of Deterministic Policies for Certain Stochastic Control Problems with Multiple Criteria and Constraints....Pages 137-148
Higher-Order Calculus of Variations on Time Scales....Pages 149-159
Finding Invariants of Group Actions on Function Spaces, a General Methodology from Non-Abelian Harmonic Analysis....Pages 161-186
Nonholonomic Interpolation for Kinematic Problems, Entropy and Complexity....Pages 187-210
Instalment Options: A Closed-Form Solution and the Limiting Case....Pages 211-229
Existence and Lipschitzian Regularity for Relaxed Minimizers....Pages 231-250
Pricing of Defaultable Securities under Stochastic Interest....Pages 251-263
Spline Cubatures for Expectations of Diffusion Processes and Optimal Stopping in Higher Dimensions (with Computational Finance in View)....Pages 265-291
An Approximate Solution for Optimal Portfolio in Incomplete Markets....Pages 293-310
Carleman Linearization of Linearly Observable Polynomial Systems....Pages 311-323
Observability of Nonlinear Control Systems on Time Scales - Sufficient Conditions....Pages 325-335
Sufficient Optimality Conditions for a Bang-bang Trajectory in a Bolza Problem....Pages 337-357
Modelling Energy Markets with Extreme Spikes....Pages 359-375
Generalized Bayesian Nonlinear Quickest Detection Problems: On Markov Family of Sufficient Statistics....Pages 377-386
Necessary Optimality Condition for a Discrete Dead Oil Isotherm Optimal Control Problem....Pages 387-395
Managing Operational Risk: Methodology and Prospects....Pages 397-417
Back Matter....Pages 419-420
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