Hostname: page-component-7857688df4-p2b9w Total loading time: 0 Render date: 2025-11-16T17:52:57.795Z Has data issue: false hasContentIssue false
  • English
  • Français

The sound of silence: equilibrium filtering and optimal censoring in financial markets

Part of: Mathematical finance Stochastic systems and control Stochastic processes

Published online by Cambridge University Press:  25 July 2016

Miles B. Gietzmann  and
Adam J. Ostaszewski
Miles B. Gietzmann*
Affiliation:
Bocconi University
Adam J. Ostaszewski*
Affiliation:
London School of Economics
*
Accounting Department, Bocconi University, Via Roentgen 1 ‒ 5o piano, Milan, Italy. Email address: miles.gietzmann@unibocconi.it
Mathematics Department, London School of Economics, Houghton Street, London WC2A 2AE, UK. Email address: a.j.ostaszewski@lse.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Following the approach of standard filtering theory, we analyse investor valuation of firms, when these are modelled as geometric-Brownian state processes that are privately and partially observed, at random (Poisson) times, by agents. Tasked with disclosing forecast values, agents are able purposefully to withhold their observations; explicit filtering formulae are derived for downgrading the valuations in the absence of disclosures. The analysis is conducted for both a solitary firm and m co-dependent firms.

Keywords

Disclosure; filteringpublic filtrationpredictable valuationoptimal censorasset price dynamics

MSC classification

Primary: 91G50: Corporate finance
Secondary: 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems) 93E11: Filtering 93E35: Stochastic learning and adaptive control 60G35: Signal detection and filtering 60G25: Prediction theory

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue A: Probability, Analysis and Number Theory , July 2016 , pp. 119 - 144
Copyright
Copyright © Applied Probability Trust 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1] Aggoun, L. and Elliott, R. J. (2004).Measure Theory and Filtering: Introduction and Applications.Cambridge University Press.CrossRefGoogle Scholar
[2] Bain, A. and Crisan, D. (2009).Fundamentals of Stochastic Filtering (Stoch. Model. Appl. Prob. 60).Springer,New York.CrossRefGoogle Scholar
[3] Bingham, N. H. and Fry, J. M. (2010).Regression: Linear Models in Statistics.Springer,London.CrossRefGoogle Scholar
[4] Bingham, N. H. and Kiesel, R. (2004).Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives,2nd edn.Springer,London.CrossRefGoogle Scholar
[5] Björk, T. and Murgoci, A. (2014).A theory of Markovian time-inconsistent stochastic control in discrete time.Finance Stoch. 18,545–592.CrossRefGoogle Scholar
[6] Brody, D. C.,Hughston, L. P. and Macrina, A. (2008).Information-based asset pricing.Internat. J. Theoret. Appl. Finance 11,107–142.CrossRefGoogle Scholar
[7] Calzolari, A. and Nappo, G. (2001).The filtering problem in a model with grouped data and counting observation times. Preprint.Google Scholar
[8] Cox, D. R. and Solomon, P. J. (2003).Components of Variance (Monogr. Statist. Appl. Prob. 97).Chapman & Hall/CRC,Boca Raton, FL.Google Scholar
[9] Daley, D. J. and Vere-Jones, D. (2003).An Introduction to the Theory of Point Processes, Vol. I,2nd edn.Springer,New York.Google Scholar
[10] Daley, D. J. and Vere-Jones, D. (2008).An Introduction to the Theory of Point Processes, Vol. II,2nd edn.Springer,New York.CrossRefGoogle Scholar
[11] Dana, R.-A. and Jeanblanc, M. (2003).Financial Markets in Continuous Time.Springer,Berlin.CrossRefGoogle Scholar
[12] Davis, M. H. A. (1984).Lectures on Stochastic Control and Nonlinear Filtering.Springer,Berlin.Google Scholar
[13] Davis, M. H. A. (1984).Piecewise-deterministic Markov processes: a general class of non-diffusion stochastic models.J. R. Statist. Soc. B 46,353–388.Google Scholar
[14] Dye, R. A. (1985).Disclosure of nonproprietary information.J. Accounting Res. 23,123–145.CrossRefGoogle Scholar
[15] Feldman, D. (1992).Logarithmic preferences, myopic decisions, and incomplete information.J. Financial Quant. Anal. 27,619–629.CrossRefGoogle Scholar
[16] Gietzmann, M. B. and Ostaszewski, A. J. (2014).Multi-firm voluntary disclosures for correlated operations.Ann. Finance 10,1–45.CrossRefGoogle Scholar
[17] Gietzmann, M. B. and Ostaszewski, A. J. (2014).Why managers with low forecast precision select high disclosure intensity: an equilibrium analysis.Rev. Quant. Finance Accounting 43,121–153.CrossRefGoogle Scholar
[18] Gietzmann, M. B. and Ostaszewski, A. J. (2016).The sound of silence: equilibrium filtering and optimal censoring in financial markets. Preprint. Available at http://arxiv.org/abs/1606.04039v1.Google Scholar
[19] Grossman, S. J. and Hart, O. D. (1980).Disclosure laws and takeover bids.J. Finance 35,323–334.CrossRefGoogle Scholar
[20] Imer, O. C. and Başa, T. (2005).Optimal estimation with limited measurements. In Proc. 44th IEEE Conf. on Decision and Control, pp. 1029–1034.CrossRefGoogle Scholar
[21] Jung, W.-O. and Kwon, Y. K. (1988).Disclosure when the market is unsure of information endowment of managers.J. Accounting Res. 26,146–153.CrossRefGoogle Scholar
[22] Kendall, M. G. and Stuart, A. (1979).The Advanced Theory of Statistics, Vol. 2: Inference and Relationship,4th edn.Griffin,London.Google Scholar
[23] Kendall, M. G. and Stuart, A. (1976).The Advanced Theory of Statistics, vol. 3: Design and Analysis, and Time Series,3rd edn.Hafner Press,New York.Google Scholar
[24] Krasa, S. and Villamil, A. P. (1994).Optimal multilateral contracts.Economic Theory 4,167–187.CrossRefGoogle Scholar
[25] Kurtz, T. G. and Nappo, G. (2011).The filtered martingale problem. In Oxford Handbook of Nonlinear Filtering, eds D. Crisan and B. Rozovskii,Oxford University Press, pp. 129–165.Google Scholar
[26] Liptser, R. S. and Shiryaev, A. N. (2001).Statistics of Random Processes (Stoch. Model. Appl. Prob. 5--6), Vols. 1--2,2nd edn.Springer,Berlin.Google Scholar
[27] Marinovic, I. and Varas, F. (2014).The timing and frequency of corporate disclosures. Working paper, Fuqua School of Business, Duke University, Durham, NC.CrossRefGoogle Scholar
[28] McNeil, A. J.,Frey, R. and Embrechts, P. (2005).Quantitative Risk Management: Concepts, Techniques and Tools.Princeton University Press.Google Scholar
[29] Ostaszewski, A. J. and Gietzmann, M. B. (2008).Value creation with Dye's disclosure option: optimal risk-shielding with an upper tailed disclosure strategy.Rev. Quant. Finance Accounting 31,1–27.CrossRefGoogle Scholar
[30] Shin, H. S. (2006).Disclosure risk and price drift.J. Accounting Res. 44,351–379.CrossRefGoogle Scholar
[31] Sinopoli, B. et al. (2004).Kalman filtering with intermittent observations.IEEE Trans. Automatic Control 49,1453–1464.CrossRefGoogle Scholar
[32] Townsend, R. M. (1979).Optimal contracts and competitive markets with costly state verification.J. Econom. Theory 21,265–293.CrossRefGoogle Scholar