Mathematical Control Theory and Finance 1st Edition by Manuel Guerra,Andrey Sarychev,Albert Shiryaev 9783540695325 354069532X

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 ISBN 10:354069532X

ISBN 13: 9783540695325

Author:Manuel Guerra,Andrey Sarychev,Albert Shiryaev

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.

Mathematical Control Theory and Finance 1st Table of contents: 

Extremals Flows and Infinite Horizon Optimization

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 on 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

 

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