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Insider information and its relation with the arbitrage condition and the utility maximization problem

Department of Statistics, Madrid University Carlos III, Avenida de la Universidad 30, 28911 Leganés, Madrid (Spain)

Special Issues: Advances in Stochastic processes and Applications

Within the well-known framework of financial portfolio optimization, we analyze the existing relationships between the condition of arbitrage and the utility maximization in presence of insider information. We assume that, since the initial time, the information flow is altered by adding the knowledge of an additional random variable including future information. In this context we study the utility maximization problem under the logarithmic and the Constant Relative Risk Aversion (CRRA) utilities, with and without the restriction of no temporary-bankruptcy.
In particular, we show that the value of the insider information may be bounded while the arbitrage condition holds and we prove that the insider information does not always imply arbitrage for the insider by providing an explicit example.
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Keywords optimal portfolio; enlargement of filtration; value of the information; arbitrage; No Free Lunch Vanishing Risk; risk neutral measure

Citation: Bernardo DAuria, José Antonio Salmerón. Insider information and its relation with the arbitrage condition and the utility maximization problem. Mathematical Biosciences and Engineering, 2020, 17(2): 998-1019. doi: 10.3934/mbe.2020053

References

  • 1. R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case, Rev. Econ. Stat., 51 (1969), 247-257.
  • 2. R. C. Merton, Optimum consumption and portfolio rules in a continuous-time model, J. Econ. Theory, 3 (1971), 373-413.
  • 3. T. Jeulin and M. Yor, Nouveaux résultats sur le grossissement des tribus, Ann. Sci. Éc. Norm. Supér., 11 (1978), 429-443.
  • 4. J. Jacod, Grossissement Initial, Hypothése (H') et Théoréme de Girsanov, Springer, 1985.
  • 5. M. Chaleyat-Maurel and T. Jeulin, Grossissement gaussien de la filtration brownienne, in Grossissements de filtrations: Exemples et applications (eds. T. Jeulin and M. Yor), Springer Berlin Heidelberg, Berlin, Heidelberg, 1985, 59-109.
  • 6. H. Föllmer and P. Imkeller, Anticipation cancelled by a girsanov transformation: A paradox on wiener space, Ann. Inst. Henri Poincaré Probab. Stat., 29 (1993), 569-586.
  • 7. I. Pikovsky and I. Karatzas, Anticipative portfolio optimization, Adv. Appl. Probab., 28 (1996), 1095-1122.
  • 8. A. Grorud and M. Pontier, Insider trading in a continuous time market model, Int. J. Theor. Appl. Finance, 01 (1998), 331-347.
  • 9. J. Amendinger, P. Imkeller and M. Schweizer, Additional logarithmic utility of an insider, Stochastic Process Appl., 75 (1998), 263-286.
  • 10. J. Amendinger, D. Becherer and M. Schweizer, A monetary value for initial information in portfolio optimization, Finance Stoch., 7 (2003), 29-46.
  • 11. S. Ankirchner, S. Dereich and P. Imkeller, The shannon information of filtrations and the additional logarithmic utility of insiders, Ann. Probab., 34 (2006), 743-778.
  • 12. F. Baudoin and L. Nguyen-Ngoc, The financial value of a weak information on a financial market, Finance Stoch., 8 (2004), 415-435.
  • 13. F. Biagini and B. Øksendal, A general stochastic calculus approach to insider trading, Appl. Math. Optim., 52 (2005), 167-181.
  • 14. A. Aksamit and M. Jeanblanc, Enlargement of Filtration with Finance in View, Springer International Publishing, 2017.
  • 15. S. Ankirchner and P. Imkeller, Finite utility on financial markets with asymmetric information and structure properties of the price dynamics, Ann. Inst. Henri Poincare Probab. Stat., 41 (2005), 479-503.
  • 16. B. Acciaio, C. Fontana and C. Kardaras, Arbitrage of the first kind and filtration enlargements in semimartingale financial models, Stochastic Process. Appl., 126 (2016), 1761-1784.
  • 17. H. N. Chau, A. Cosso and C. Fontana, The value of informational arbitrage, preprint, URL https://arxiv.org/abs/1804.00442.
  • 18. H. N. Chau, W. Runggaldier and P. Tankov, Arbitrage and utility maximization in market models with an insider, Math. Financ. Econ., 12 (2018), 589-614.
  • 19. F. Delbaen, Representing martingale measures when asset prices are continuous and bounded, Math. Finance, 2 (1992), 107-130.
  • 20. P. Imkeller, Random times at which insiders can have free lunches, Stoch. Stoch. Rep., 74 (2002), 465-487.
  • 21. C. Fontana, M. Jeanblanc and S. Song, On arbitrages arising with honest times, Finance Stoch., 18 (2014), 515-543.
  • 22. C. Kardaras, On the characterisation of honest times that avoid all stopping times, Stochastic Process. Appl., 124 (2014), 373-384.
  • 23. F. Delbaen and W. Schachermayer, A general version of the fundamental theorem of asset pricing, Math. Ann., 300 (1994), 463-520.
  • 24. F. Delbaen and W. Schachermayer, The Mathematics of Arbitrage, Springer Finance, SpringerVerlag, 2006.
  • 25. F. Baudoin, Conditioned stochastic differential equations: Theory, examples and application to finance, Stochastic Process. Appl., 100 (2002), 109-145.    
  • 26. P. Imkeller, M. Pontier and F. Weisz, Free lunch and arbitrage possibilities in a financial market model with an insider, Stochastic Process. Appl., 92 (2001), 103-130.
  • 27. N. Bauerle and U. Rieder, Portfolio optimization with markov-modulated stock prices and interest rates, IEEE Trans. Automat. Control, 15 (2004), 442-447.
  • 28. K. Itô, Extension of stochastic integrals, in Proceedings of International Symposium on Stochastic Differential Equations (Kyoto University, 1976), Wiley, New York, USA, 1978, 95-109.
  • 29. P. E. Protter, Stochastic Integration and Differential Equations, Springer Berlin Heidelberg, 2005.
  • 30. S. Dragomir and R. Agarwa, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, App. Math. Lett., 11 (1997), 91-95.

 

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