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References

  1. S.Albeverio, J.E.Fenstad, R.H¯egh-Krohn, and T.Lindstr¯m, Nonstandard methods in stochastic analysis and mathematical physics, Academic Press, Orlando, 1986.
  2. N.H.Bingham and R.Kiesel, Risk-neutral valuation: Pricing and hedging of financial derivatives, Springer-Verlag, London, 1998. Math.Review2000a:91057
  3. N.J.Cutland, P.E.Kopp, and W.Willinger, A nonstandard approach to option pricing, Mathematical Finance 1 (1991), no.4, 1-38.
  4. N.J.Cutland, P.E.Kopp, and W.Willinger, From discrete to continuous financial models: New convergence results for option pricing, Mathematical Finance 3 (1993), no.2, 101-123.
  5. N.J.Cutland, P.E.Kopp, and W.Willinger, A nonstandard treatment of options driven by Poisson processes, Stochastics and Stochastics Reports 42 (1993), 115-133. Math. Review 95a:90009
  6. N.J.Cutland, P.E.Kopp, and W.Willinger, From discrete to continuous stochastic calculus, Stochastics and Stochastics Reports 52 (1995), no.3+4, 173-192. Math. Review 97d:60093
  7. L.Clewlow and C.Strickland, Implementing derivatives models, John Wiley & Sons, 1998.
  8. N.J.Cutland, Infinitesimals in action, Journal of the London Mathematical Society 35 (1987), 202-216. Math.Review88d:26045
  9. N.J.Cutland, Loeb measures in practice: Recent advances, EMS Lectures 1997, Springer-Verlag, 2000.
  10. D.Duffie and P.Protter, From discrete- to continuous-time finance: Weak convergence of the financial gain process, Mathematical Finance 2 (1992), 1-15.
  11. R.J.Elliott, Stochastic calculus and applications, Springer-Verlag, New York, 1982. Math. Review 85b:60059
  12. H.Fˆllmer and M.Schweizer, Hedging of contingent claims under incomplete information, Applied Stochastic Analysis (M.H.A. Davis and R.J. Elliott, eds.), Gordon and Breach, London, 1991, pp.389-414. Math.Review92g:90029
  13. D.N.Hoover and E.Perkins, Nonstandard construction of the stochastic integral and applications to stochastic differential equations. I+II, Transactions of the American Mathematical Society 275 (1983), no.1, 1-58. Math.Review85d:60111
  14. A.Jakubowski, J.MÈmin, and G.Pages, Convergence en loi des suites d'intÈgrales stochastiques sur l'espace D1 de Skohorod, Probability Theory and Related Fields 81 (1989), 111-137. Math.Review90e:60065
  15. M.Musiela and M.Rutkowski, Martingale methods in financial modelling, Springer-Verlag, New York, 1997. Math.Review98i:90014
  16. P.Monat and C.Stricker, Fˆllmer-Schweizer decomposition and mean-variance hedging for general claims, Annals of Probability 23 (1995), 605-628. Math. Review 97m:60065
  17. F.Mercurio and T.C.F.Vorst, Option pricing with hedging at fixed trading dates, Applied Mathematical Finance 3 (1996), no.2, 135-158.
  18. J.L. Prigent, Incomplete markets: Convergence of option values under the minimal martingale measure, THEMA preprint no.9735, UniversitÈ de Cergy-Pontoise, November 1997, forthcoming in Advances in Applied Probability.
  19. W.J.Runggaldier and M.Schweizer, Convergence of option values under incompleteness, Seminar on Stochastic Analysis, Random Fields and Applications (E.Bolthausen, M.Dozzi, and F.Russo, eds.), Birkh‰user Verlag, 1995, pp.365-384. Math. Review 97j:60092
  20. M.Schweizer, Hedging of options in a general semimartingale model, PhD thesis, ETH Z¸rich, 1988.
  21. M.Schweizer, Risk-minimality and orthogonality of martingales, Stochastics and Stochastics Reports 30 (1990), 123-131.
  22. M.Schweizer, Option hedging for semimartingales, Stochastic Processes and their Applications 37 (1991), 339-363. Math.Review92c:90025
  23. M.Schweizer, Variance-optimal hedging in discrete time, Mathematics of Operations Research 20 (1993), 1-32.
  24. M.Sch‰l, On quadratic cost criteria for option hedging, Mathematics of Operations Research 19 (1994), 121-131.
  25. M.Schweizer, Approximating random variables by stochastic integrals, Annals of Probability 22 (1994), no.3, 1536-1575.
  26. M.S.Taqqu and W.Willinger, The analysis of finite security markets using martingales, Advances in Applied Probability 18 (1987), 1-25. Math.Review88c:90032
  27. V.Wellmann, Convergence in incomplete market models, PhD thesis, University of Hull, 1998, http://www.wellmann.clara.net.
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