Mathematical Control Theory and Finance

1. Front Matter

   Pages I-XIII

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2. Extremals Flows and Infinite Horizon Optimization

   • Andrei A. Agrachev, Francesca C. Chittaro

   Pages 1-13

3. Laplace Transforms and the American Call Option

   • Ghada Alobaidi, Roland Mallier

   Pages 15-27

4. Time Change, Volatility, and Turbulence

   • Ole E. Barndorff-Nielsen, Jürgen Schmiegel

   Pages 29-53

5. External Dynamical Equivalence of Analytic Control Systems

   • Zbigniew Bartosiewicz, Ewa Pawłuszewicz

   Pages 55-69

6. On Option-Valuation in Illiquid Markets: Invariant Solutions to a Nonlinear Model

   • Ljudmila A. Bordag

   Pages 71-94

7. Predicting the Time of the Ultimate Maximum for Brownian Motion with Drift

   • Jacques du Toit, Goran Peskir

   Pages 95-112

8. A Stochastic Demand Model for Optimal Pricing of Non-Life Insurance Policies

   • Paul Emms

   Pages 113-136

9. Optimality of Deterministic Policies for Certain Stochastic Control Problems with Multiple Criteria and Constraints

   • Eugene A. Feinberg

   Pages 137-148

10. Higher-Order Calculus of Variations on Time Scales

    • Rui A. C. Ferreira, Delfim F. M. Torres

    Pages 149-159

11. Finding Invariants of Group Actions on Function Spaces, a General Methodology from Non-Abelian Harmonic Analysis

    • Jean-Paul Gauthier, Fethi Smach, Cedric Lemaître, Johel Miteran

    Pages 161-186

12. Nonholonomic Interpolation for Kinematic Problems, Entropy and Complexity

    • Jean-Paul Gauthier, Vladimir Zakalyukin

    Pages 187-210

13. Instalment Options: A Closed-Form Solution and the Limiting Case

    • Susanne Griebsch, Christoph Kühn, Uwe Wystup

    Pages 211-229

14. Existence and Lipschitzian Regularity for Relaxed Minimizers

    • Manuel Guerra, Andrey Sarychev

    Pages 231-250

15. Pricing of Defaultable Securities under Stochastic Interest

    • Nino Kordzakhia, Alexander Novikov

    Pages 251-263

16. Spline Cubatures for Expectations of Diffusion Processes and Optimal Stopping in Higher Dimensions (with Computational Finance in View)

    • Andrew Lyasoff

    Pages 265-291

17. An Approximate Solution for Optimal Portfolio in Incomplete Markets

    • Francesco Menoncin

    Pages 293-310

18. Carleman Linearization of Linearly Observable Polynomial Systems

    • Dorota Mozyrska, Zbigniew Bartosiewicz

    Pages 311-323

19. Observability of Nonlinear Control Systems on Time Scales - Sufficient Conditions

    • Ewa Pawłuszewicz

    Pages 325-335

20. Sufficient Optimality Conditions for a Bang-bang Trajectory in a Bolza Problem

    • Laura Poggiolini, Marco Spadini

    Pages 337-357

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.

• Deterministic Control
• Finance
• Interpolation
• Stochastic Control
• calculus
• entropy
• incomplete markets
• mathematical finance
• mathematics
• modeling
• optimal control
• optimization
• volatility
• quantitative finance

• DiMaD, University of Florence, Florence, Italy

  Andrey Sarychev

• Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

  Albert Shiryaev

• ISEG-TU Lisbon, Lisbon, Portugal

  Manuel Guerra, Maria do Rosário Grossinho

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