Skip to main content
Log in

Some applications of stochastic analysis in financial economics: An outline

  • Published:
Rivista di matematica per le scienze economiche e sociali Aims and scope Submit manuscript

Abstract

The basic features of a recent approach to the theory of continuous trading, are presented.

Sommario

Vengono presentate le linee base di un recente approccio alle opzioni in tempo continuo basato su tecniche di analisi stocastica.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bachelier L.,Théorie de la Spéculation, Thesis for the Doctorate in Mathematical Sciences, Ann. Sci. Ecole Norm. Sup., III-17, 1900, 21–86.

    Google Scholar 

  2. Back, K., Pliska S.R.,On the fundamental theorem of asset pricing with an infinite state space. J. Math. Econom., 20, 1991, 1–18.

    Article  Google Scholar 

  3. Bensoussan A.,On the Theory of option pricing, Acta Appl. Math., 2, 1984, 139–158.

    Google Scholar 

  4. Black F., Scholes M.,The pricing of options and corporate liabilities, J. Polit. Econom., 81, 1973, 637–659.

    Article  Google Scholar 

  5. Di Masi G. B., Platen E., Runggaldier W. J.,Pricing of options on assets with markovian volatilities under discrete observation, 1992, preprint.

  6. Duffie D.,Stochastic equilibria: existence, spanning number, and the ‘no expected financial gain form trade’ hypothesis”, Econometrica, 54, 1986, 1161–1183.

    Google Scholar 

  7. Duffie D.,Security Markets: Stochastic Models, Boston, Academic Press, 1988.

    Google Scholar 

  8. Föllmer H., Schweizer M.,Hedging of contingent claims under incomplete information. In Applied Stochastic Analysis (M. H. A. Davis and R. J. Elliot, eds.), Stochastic Monographs, Gordon and Breach, New York, 5, 1991, 389–414.

    Google Scholar 

  9. Harrison J. M., Kreps D. M.,Martingales and arbitrage in multiperiod securities markets, J. Econom. Theory, 20, 1979, 381–408.

    Article  Google Scholar 

  10. Harrison J. M., Pliska S. R.,Martingales and stochastic integrals in the theory of contnuous trading, Stoch. Proc. Appl., 11, 1981, 215–260.

    Article  Google Scholar 

  11. Harrison J. M., Pliska S. R.,A stochastic calculus model of continuous trading: complete markets, Stoch. Proc. Appl., 15, 1983, 313–316.

    Article  Google Scholar 

  12. Huang C.-F.,Information structure and equilibrium prices, J. Econom. Theory, 35, 1985, 33–71.

    Article  Google Scholar 

  13. Ikeda N., Watanabe S.,Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981.

    Google Scholar 

  14. Jeanblanc-Picque M., Pontier M.,Optimal portfolio for a small investor in a market model with discontinuous prices, Appl. Math. Optim., 22, 1990, 287–310.

    Article  Google Scholar 

  15. Karatzas I.,On the pricing of American options, Appl. Math. Optim., 17, 1988, 37–60.

    Article  Google Scholar 

  16. Karatzas I.,Optimization problems in the theory of continuous trading, SIAM J. Control Optim., 27, 1989, 1221–1259.

    Article  Google Scholar 

  17. Karatzas I., Lehoczky J. P., Shreve S. E.,Optimal portfolio and consumption decisions for a ‘small investor’ on a finite horizon, SIAM J. Control Optim., 25, 1987, 1557–1586.

    Article  Google Scholar 

  18. Karatzas I., Lehoczky J. P., Shreve S. E.,Existence and uniqueness of multi-agent equilibrium in a stochastic, dynamic consumption/investment model, Math. Oper. Res., 15, 1990, 80–128.

    Google Scholar 

  19. Kind P., Liptser R. Sh., Runggaldier W. J.,Diffusion approximation in past dependent models and applications to option pricing, Ann. Appl. Probab., 1, 1991, 379–405.

    Google Scholar 

  20. Mercurio F., Runggaldier W. J.,Option pricing for jump diffusion: approximations and their interpretation, Math. Finance, 3, 1993, 191–200.

    Google Scholar 

  21. Metivier M.,Semimartingales, a Course on Stochastic Processes, W. de Gruyter, Berlin-New York, 1982.

    Google Scholar 

  22. Samuelson P. A.,Rational theory of warrant pricing, Ind. Management Rev., 6, 1965, 13–39.

    Google Scholar 

  23. Schweizer M.,Hedging of options in a general semimartingale model, Diss. ETHZ n. 8615, Zürich, 1988.

  24. Schweizer M.,Option hedging for semimartingales, Stoch. Proc. Appl., 37, 1991, 339–363.

    Article  Google Scholar 

  25. Stricker C.,Integral representation in the theory of continuous trading, Stochastics and Stochastic Reports, 13, 1984, 249–255.

    Google Scholar 

  26. Stricker C.,Arbitrage et lois de martingale, Ann. Inst. Henri Poincaré, 26, 1990, 451–460.

    Google Scholar 

  27. Willinger W., Taqqu M. S.,Pathwise stochastic integration and applications to the theory of continuous trading, Stoch. Proc. Appl., 32, 1989, 253–280.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zanzotto, P.A. Some applications of stochastic analysis in financial economics: An outline. Rivista di Matematica per le Scienze Economiche e Sociali 18, 181–198 (1995). https://doi.org/10.1007/BF02096427

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02096427

Keywords

Navigation