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Mathematical Control Theory and Finance (eBook)

Andrey Sarychev, Albert Shiryaev, Manuel Guerra, Maria do Rosário Grossinho (Herausgeber)

eBook Download: PDF

2009 | 2008
XIII, 420 Seiten
Springer Berlin (Verlag)
978-3-540-69532-5 (ISBN)

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Control theory provides a large set of theoretical and computational tools with applications in a wide range of ?elds, running from 'pure' branches of mathematics, like geometry, to more applied areas where the objective is to ?nd solutions to 'real life' problems, as is the case in robotics, control of industrial processes or ?nance. The 'high tech' character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the ?nancial analyst to possess a high level of mathematical skills. C- versely, the complex challenges posed by the problems and models relevant to ?nance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical ?nance. Up to now, other branches of control theory have found comparatively less application in ?n- cial problems. To some extent, deterministic and stochastic control theories developed as di?erent branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these ?elds has intensi?ed. Some concepts from stochastic calculus (e.g., rough paths) havedrawntheattentionofthedeterministiccontroltheorycommunity.Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to stochastic c- trol.

Preface 5
Contents 7
List of Contributors 10
Extremals Flows and In.nite Horizon Optimization 13
Laplace Transforms and the American Call Option 26
Time Change, Volatility, and Turbulence 39
External Dynamical Equivalence of Analytic Control Systems 64
On Option-Valuation in Illiquid Markets: Invariant Solutions to a Nonlinear Model 79
Predicting the Time of the Ultimate Maximum for Brownian Motion with Drift 103
A Stochastic Demand Model for Optimal Pricing of Non- Life Insurance Policies 121
Optimality of Deterministic Policies for Certain Stochastic Control Problems with Multiple Criteria and Constraints 145
Higher-Order Calculus of Variations on Time Scales 157
Finding Invariants of Group Actions on Function Spaces, a General Methodology from Non- Abelian Harmonic Analysis 168
Nonholonomic Interpolation for Kinematic Problems, Entropy and Complexity 194
Instalment Options: A Closed-Form Solution and the Limiting Case 218
Existence and Lipschitzian Regularity for Relaxed Minimizers 237
Pricing of Defaultable Securities under Stochastic Interest 257
Spline Cubatures for Expectations of Di.usion Processes and Optimal Stopping in Higher Dimensions ( with Computational Finance in View) 270
An Approximate Solution for Optimal Portfolio in Incomplete Markets 297
Carleman Linearization of Linearly Observable Polynomial Systems 315
Observability of Nonlinear Control Systems on Time Scales - Sufficient Conditions 328
Sufficient Optimality Conditions for a Bang- bang Trajectory in a Bolza Problem 339
Modelling Energy Markets with Extreme Spikes 360
Generalized Bayesian Nonlinear Quickest Detection Problems: On Markov Family of Sufficient Statistics 377
Necessary Optimality Condition for a Discrete Dead Oil Isotherm Optimal Control Problem 387
Managing Operational Risk: Methodology and Prospects 396
Workshop on Mathematical Control Theory and Finance 417

Erscheint lt. Verlag	31.3.2009
Zusatzinfo	XIII, 420 p.
Verlagsort	Berlin
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Statistik
	Technik
	Wirtschaft ► Allgemeines / Lexika
	Wirtschaft ► Betriebswirtschaft / Management ► Finanzierung
Schlagworte	Calculus • Deterministic Control • Entropy • Finance • incomplete markets • Interpolation • mathematical finance • Mathematics • Modeling • optimal control • Optimization • Quantitative Finance • stochastic control • Volatility
ISBN-10	3-540-69532-X / 354069532X
ISBN-13	978-3-540-69532-5 / 9783540695325

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