The Journal of Geometric Mechanics (JGM)

Geometric arbitrage theory and market dynamics
Pages: 431 - 471, Issue 4, December 2015

doi:10.3934/jgm.2015.7.431      Abstract        References        Full text (672.4K)           Related Articles

Simone Farinelli - Core Dynamics GmbH, Scheuchzerstrasse 43, CH-8006, Zurich, Switzerland (email)

1 V. I. Arnold, Mathematical Methods of Classical Mechanics, Graduate Texts in Mathematics, Second Edition, Springer, 1989.       
2 F. Bellini and M. Frittelli, On the existence of minimax martingale measures, Mathematical Finance, 12 (2002), 1-21.       
3 T. Björk, Arbitrage Theory in Continuous Time, Oxford Finance, Second Edition, 2004.
4 T. Björk and H. Hult, A note on Wick products and the fractional Black-Scholes model, Finance & Stochastics, 9 (2005), 197-209.       
5 D. Bleecker, Gauge Theory and Variational Principles, Addison-Wesley Publishing, 1981, (republished by Dover 2005).       
6 J. Cresson and S. Darses, Stochastic embedding of dynamical systems, J. Math. Phys., 48 (2007), 072703, 54 pp.       
7 F. Delbaen and W. Schachermayer, The Mathematics of Arbitrage, Springer-Verlag, Berlin, 2006.       
8 B. A. Dubrovin, A. T. Fomenko and S. P. Novikov, Modern Geometry-Methods and Applications: Part II. The Geometry and Topology of Manifolds, Graduate Texts in Mathematics, 104. Springer-Verlag, New York, 1985.       
9 B. Dupoyet, H. R. Fiebig and D. P. Musgrov, Gauge invariant lattice quantum field theory: Implications for statistical properties of high frequency financial markets, Physica A, 389 (2010), 107-116.
10 C. Dellachérie and P. A. Meyer, Probabilité et Potentiel II - Théorie des Martingales - Chapitres 5 à 8, Hermann, 1980.       
11 K. D. Elworthy, Stochastic Differential Equations on Manifolds, London Mathematical Society Lecture Notes Series, 1982.       
12 M. Eméry, Stochastic Calculus on Manifolds-With an Appendix by P. A. Meyer, Springer, 1989.       
13 S. Farinelli and S. Vazquez, Gauge invariance, geometry and arbitrage, The Journal of Investment Strategies, Wiley, Spring, 1 (2012), 23-66.
14 M. Fei-Te and M. Jin-Long, Solitary wave solutions of nonlinear financial markets: Data-modeling-concept-practicing, Front. Phys. China, 2 (2007), 368-374.
15 B. Flesaker and L. Hughston, Positive Interest, Risk, 9 (1996), 36-40.
16 H. Föllmer and A. Schied, Stochastic Finance: An Introduction In Discrete Time, Second Edition, De Gruyter Studies in Mathematics, 2004.       
17 Y. E. Gliklikh, Global and Stochastic Analysis with Applications to Mathematical Physics, Theoretical and Mathemtical Physics, Springer, 2011.       
18 W. Hackenbroch and A. Thalmaier, Stochastische Analysis. Eine Einführung in die Theorie der stetigen Semimartingale, Teubner Verlag, 1994.       
19 L. Hörmander, The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis, Springer, 2003.       
20 E. P. Hsu, Stochastic Analysis on Manifolds, Graduate Studies in Mathematics, 38, AMS, 2002.       
21 P. J. Hunt and J. E. Kennedy, Financial Derivatives in Theory and Practice, Wiley Series in Probability and Statistics, 2004.       
22 K. Ilinski, Gauge geometry of financial markets, J. Phys. A: Math. Gen., 33 (2000), L5-L14.       
23 K. Ilinski, Physics of Finance: Gauge Modelling in Non-Equilibrium Pricing, Wiley, 2001.
24 J. D. Jackson, Classical Electrodynamics, Third Edition, Wiley, 1998.
25 S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Volume I, Wiley, 1996.       
26 P. N. Malaney, The Index Number Problem: A Differential Geometric Approach, PhD Thesis, Harvard University Economics Department, 1997.       
27 Y. Morisawa, Toward a geometric formulation of triangular arbitrage: An introduction to gauge theory of arbitrage, Progress of Theoretical Physics Supplement, 179 (2009), 209-215.
28 E. Nelson, Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, N.J. 1967.       
29 Ph. E. Protter, Stochastic Integration and Differential Equations: Version 2.1, Stochastic Modelling and Applied Probability, 21. Springer-Verlag, Berlin, 2005.       
30 L. C. G. Rogers, Equivalent martingale measures and no-arbitrage, Stochastics, Stochastics Rep., 51 (1994), 41-49.       
31 W. Schachermayer, Optimal investment in incomplete markets when wealth may become negative, Annals of Applied Probability, 11 (2001), 694-734.
32 L. Schwartz, Semi-martingales Sur des Variétés et Martingales Conformes sur des Variétés Analytiques Complexes, Springer Lecture Notes in Mathematics, 1980.       
33 S. E. Shreve, Stochastic Calculus for Finance, Springer-Verlag, New York, 2004.       
34 M. Šilhavý, The Mechanics and Thermodynamics of Continuous Media, Texts and Monographs in Physics. Springer-Verlag, Berlin, 1997.       
35 A. Smith and C. Speed, Gauge Transforms in Stochastic Investment, Proceedings of the 1998 AFIR Colloquim, Cambridge, England, 1998.
36 S. Sternberg, Lectures On Differential Geometry, Second Edition, Chelsea Publishing Co., New York, 1983.       
37 D. W. Stroock, An Introduction to the Analysis of Paths on a Riemannian Manifold, Mathematical Surveys and Monographs, 74, AMS, 2000.       
38 E. Weinstein, Gauge theory and inflation: Enlarging the Wu-Yang Dictionary to a unifying Rosetta Stone for Geometry in Application, Talk given at Perimeter Institute, 2006.
39 K. Yasue, Stochastic calculus of variations, Journal of Functional Analysis, 41 (1981), 327-340.       
40 K. Young, Foreign exchange market as a lattice gauge theory, Am. J. Phys., 67 (1999), p862.

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