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Bubbles and Crashes

Mathematical models of bubbles

Pages 10-13 | Received 14 Dec 2015, Accepted 27 Jan 2016, Published online: 13 Jun 2016

References

  • Aït Sahalia, Y. and Jacod, J., High Frequency Financial Econometrics, 2014 (Princeton University Press: Princeton, NJ).
  • Andersen, L.B.G. and Piterbarg, V., Moment explosions in stochastic volatility models. Financ. Stoch., 2007, 11, 29–50. doi: 10.1007/s00780-006-0011-7
  • Chybiryakov, O., Itô's integrated formula for strict local martingales with jumps, Séminaire de Probabilités XL, Springer Lecture Notes in Mathematics, Vol. 1899, pp. 375–388, 2007 (Springer-Verlag: Heidelberg).
  • Dandapani, A., PhD Thesis to be completed in 2016, Statistics Department of Columbia University, in preparation.
  • Delbaen, F. and Schachermayer, W., The fundamental theorem of asset pricing for unbounded stochastic processes. Math. Ann., 1998, 312(2), 215–250. doi: 10.1007/s002080050220
  • Delbaen, F. and Shirakawa, H., No arbitrage condition for positive diffusion price processes. Asia-Pacific Financ.Markets, 2002, 9, 159–168. doi: 10.1023/A:1024173029378
  • Fontana, C., Jeanblanc, M. and Song, S., On arbitrages arising with honest times. Financ. Stoch, 2014, 18, 515–543. doi: 10.1007/s00780-014-0231-1
  • Jacod, J. and Protter, P., Strict local martingale solutions of stochastic differential equations, working paper, 2015.
  • Jarrow, R., Testing for asset price bubbles: three new approaches. Quant. Financ. Lett. 2015. http://dx.doi.org/10.1080/21649502.2016.1165863.
  • Jarrow, R., Kchia, Y. and Protter, P., How to detect an asset bubble. SIAM J. Financ. Math. 2011, 2, 839–865. doi: 10.1137/10079673X
  • Jarrow, R.A., Protter, P. and Shimbo, K., Asset price bubbles in incomplete markets. Math. Financ. 2010, 20, 145–185. doi: 10.1111/j.1467-9965.2010.00394.x
  • Herdegen, M. and Schweizer, M., Economics-based financial bubbles (and Why they imply strict local martingales), Swiss Finance Institute Research Paper No. 15-05. Available at SSRN: http://ssrn.com/abstract=2566815 or http://dx.doi.org/10.2139/ssrn.2566815, 2015.
  • Keller-Ressel, M., Simple examples of pure jump strict local martingales. Stoch. Process. Appl. 2015, 125, 4142–4153. doi: 10.1016/j.spa.2015.06.003
  • Lions, P.L. and Musiela, M., Correlations and bounds for stochastic volatility models. Annales Inst. Henri Poincaré, (C) Nonlinear Analysis, 2007, 24(1), 1–16. doi: 10.1016/j.anihpc.2005.05.007
  • Mijatović, A. and Urusov, M., On the martingale property of certain local martingales. Probab. Theory Related Fields, 2012, 152, 1–30. doi: 10.1007/s00440-010-0314-7
  • Obayashi, Y., Protter, P. and Yang, S., The lifetime of a financial bubble. Math. Financ. Econ. 2016. 10.1007/s11579-016-0170-z.
  • Protter, P., Stochastic Integration and Differential Equations, Version 2.1, 2005 (Heidelberg:Springer).
  • Protter, P., A mathematical theory of financial bubbles. In Paris-Princeton Lectures on Mathematical Finance 2013, Lecture Notes in Mathematics, edited by Vicky Henderson and Ronnie Sircar, pp. 1–108, 2013 (Heidelberg: Springer).
  • Protter, P., Strict local martingales with jumps. Stoch. Process. Appl. 2015, 125, 1352–1367. doi: 10.1016/j.spa.2014.10.018
  • Sin, C.A., Complications with stochastic volatility models. Adv. Appl. Probab. 1998, 30, 256–268. doi: 10.1239/aap/1035228003