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Information-Theoretic Approach to Financial Market Modelling

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  • Eckhard Platen

Abstract

The paper treats the financial market as a communication system, using four information-theoretic assumptions to derive an idealized model with only one parameter. State variables are scalar stationary diffusions. The model minimizes the surprisal of the market and the Kullback-Leibler divergence between the benchmark-neutral pricing measure and the real-world probability measure. The state variables, their sums, and the growth optimal portfolio of the stocks evolve as squared radial Ornstein-Uhlenbeck processes in respective activity times.

Suggested Citation

  • Eckhard Platen, 2026. "Information-Theoretic Approach to Financial Market Modelling," Papers 2602.14575, arXiv.org.
    • Handle: RePEc:arx:papers:2602.14575
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    References listed on IDEAS

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    1. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    2. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
    3. Damir Filipović & Eckhard Platen, 2009. "Consistent Market Extensions Under The Benchmark Approach," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 41-52, January.
    4. Michael Schmutz & Eckhard Platen & Thorsten Schmidt, 2025. "Benchmark-Neutral Risk-Minimization for insurance products and nonreplicable claims," Papers 2506.19494, arXiv.org.
    5. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    6. Mark Craddock & Eckhard Platen, 2003. "Symmetry Group Methods for Fundamental Solutions and Characteristic Functions," Research Paper Series 90, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    8. Eckhard Platen, 2025. "Benchmark-neutral pricing," Quantitative Finance, Taylor & Francis Journals, vol. 25(12), pages 1907-1919, December.
    9. Eckhard Platen & Renata Rendek, 2019. "Dynamics of a Well-Diversified Equity Index," Research Paper Series 398, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. Hardy Hulley & Martin Schweizer, 2010. "M6 - On Minimal Market Models and Minimal Martingale Measures," Research Paper Series 280, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. Eckhard Platen, 2025. "Pricing under the Benchmark Approach," Papers 2506.16264, arXiv.org.
    12. Platen, Eckhard, 2000. "A minimal financial market model," SFB 373 Discussion Papers 2000,91, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    13. Markowitz, Harry M & Usmen, Nilufer, 1996. "The Likelihood of Various Stock Market Return Distributions, Part 1: Principles of Inference," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 207-219, November.
    14. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    15. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    16. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    17. Robert A. Jarrow, 2022. "Correction to: Continuous-Time Asset Pricing Theory," Springer Finance, in: Continuous-Time Asset Pricing Theory, edition 2, chapter 24, pages C1-C3, Springer.
    18. Grossman, Sanford J & Stiglitz, Joseph E, 1980. "On the Impossibility of Informationally Efficient Markets," American Economic Review, American Economic Association, vol. 70(3), pages 393-408, June.
    19. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    20. B. B. Mandelbrot, 2001. "Scaling in financial prices: I. Tails and dependence," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 113-123.
    21. Aït-Sahalia, Yacine & Fan, Jianqing & Li, Yingying, 2013. "The leverage effect puzzle: Disentangling sources of bias at high frequency," Journal of Financial Economics, Elsevier, vol. 109(1), pages 224-249.
    22. W. Breymann & D. R. Lüthi & E. Platen, 2009. "Empirical behavior of a world stock index from intra-day to monthly time scales," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 71(4), pages 511-522, October.
    23. Eckhard Platen & David Heath, 2006. "A Benchmark Approach to Quantitative Finance," Springer Finance, Springer, number 978-3-540-47856-0, March.
    24. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    25. Eckhard Platen & Kevin Fergusson, 2025. "Free Lunches with Vanishing Risks Most Likely Exist," Papers 2508.07108, arXiv.org.
    26. Omar Euch & Masaaki Fukasawa & Mathieu Rosenbaum, 2018. "The microstructural foundations of leverage effect and rough volatility," Finance and Stochastics, Springer, vol. 22(2), pages 241-280, April.
    27. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    28. B. B. Mandelbrot, 2001. "Scaling in financial prices: IV. Multifractal concentration," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 641-649.
    29. Hardy Hulley & Martin Schweizer, 2010. "M6—On Minimal Market Models and Minimal Martingale Measures," Springer Books, in: Carl Chiarella & Alexander Novikov (ed.), Contemporary Quantitative Finance, pages 35-51, Springer.
    30. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    31. Markowitz, Harry M & Usmen, Nilufer, 1996. "The Likelihood of Various Stock Market Return Distributions, Part 2: Empirical Results," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 221-247, November.
    32. Eckhard Platen & Renata Rendek, 2012. "Approximating the numéraire portfolio by naive diversification," Journal of Asset Management, Palgrave Macmillan, vol. 13(1), pages 34-50, February.
    33. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    34. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

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