Martingale Measures and Hedging for Discrete-Time Financial Markets

References

• Ansel J. P. , Stricker C. Quelques remarques sur un théorème de Yan. Sem. de Probabilités. (1990) XXIV (Springer, Berlin, Germany) 266 274 . Lecture Notes in Mathematics Google Scholar
• Artzner P. , Dempster M. A. H. , Pliska S. R. On the numeraire portfolio. Mathematics of Derivative Securities (1997) (Cambridge University Press, Cambridge, Massachusetts) 216 226 Google Scholar
• Back F. , Pliska S. R. On the fundamental theorem of asset pricing with an infinite state space. J. Math. Econom. (1990) 20 1 18 Crossref, Google Scholar
• Chow Y. S. , Robbins H. , Siegmund D. Great Expectations: The Theory of Optimal Stopping (1971) (Houghton Mifflin, Boston) Google Scholar
• Cvitanic J. , Karatzas I. Hedging contingent claims with constrained portfolios. Ann. Appl. Probab. (1993) 3 652 681 Crossref, Google Scholar
• Dalang R. C. , Morton A. , Willinger W. Equivalent martingale measures and no-arbitrage in stochastic securities market models. Stochastics Stochastic Rep. (1990) 29 185 201 Crossref, Google Scholar
• Davis M. H. A. , Dempster M. A. H. , Pliska S. R. Option pricing in incomplete markets. Mathematics of Derivative Securities (1997) (Cambridge University Press, Cambridge, Massachusetts) 216 226 Google Scholar
• Delbaen F. , Schachermayer W. Mathematical theory of arbitrage. (1994) . Seminar notes, preliminary version Google Scholar
• Dubins L. E. , Sudderth W. D. Countably additive gambling and optimal stopping. Z. Wahrscheinlichkeitstheorie verw. Gebiet (1977) 41 59 72 Crossref, Google Scholar
• El Karoui N. , Jeanblanc-Picqué M. Robustness of the Black and Scholes formula. (1993) . Working paper Google Scholar
• El Karoui N. , Quenez M. C. Dynamic programming and pricing of contingent claims in an incomplete market. SIAM J. Control Optim. (1995) 33 29 66 Crossref, Google Scholar
• Fakeev A. G. Optimal stopping rules for processes with continuous parameter. Theory Probab. Appl. (1970) 15 324 331 Crossref, Google Scholar
• Föllmer H. , Kabanov Yu. M. Optional decomposition and Lagrange multipliers. Finance Stochast (1998) 2 69 81 Google Scholar
• Föllmer H. , Kramkov D. Optional decompositions under constraints. Probab. Theory Relat. Fields (1997) 190 1 25 Google Scholar
• Föllmer H. , Schweizer M. Hedging by sequential regression: An introduction to the mathematics of option trading. The ASTIN Bull. (1989) 1 147 160 Google Scholar
• Föllmer H. , Schweizer M. , Davis M. H. A. , Elliot R. J. Hedging of contingent claims under incomplete information. Applied Stochastic Analysis (1990) (Gordon and Breach, London, UK) Google Scholar
• Gerber H. U. , Shiu E. S. W. Option pricing by Esscher transforms. Trans. Soc. Actuaries (1994) 46 Google Scholar
• Harrison J. M. , Kreps D. M. Martingales and arbitrage in multiperiod securities markets. J. Econom. Theory (1979) 20 381 408 Crossref, Google Scholar
• Hinderer K. Foundations of nonstationary dynamic programming with discrete time-parameter. (1970) 33 (Springer, Berlin-Heidelberg-New York) . Lecture Notes in Operations Research and Mathematical Systems Google Scholar
• Hordijk A. Dynamic programming and Markov potential theory. Mathematical Centre Tracts (1974) 51 (Amsterdam, The Netherlands) Google Scholar
• Jacod J. , Shiryaev A. N. Local martingales and the fundamental asset pricing theorems in the discrete-time case. Finance Stochast. (1998) 3 259 273 Crossref, Google Scholar
• Karatzas I. On the pricing of American options. Appl. Math. Optim. (1988) 17 37 60 Crossref, Google Scholar
• Karatzas I. , Kou S. G. On the pricing of contingent claims under constraints. Ann. Appl. Probab. (1996) 6 321 369 Crossref, Google Scholar
• Kramkov D. O. Optional decomposition of supermartingales and hedging of contingent claims in incomplete security markets. Probab. Theory Relat. Fields (1996) 105 459 479 Crossref, Google Scholar
• Levy H. , Levy A. Option valuation: An extension of the binomial model. (1988) Conference HEC Paris Google Scholar
• Long J. The numeraire portfolio. J. Finance (1990) 44 205 209 Google Scholar
• Merton R. C. Theory of rational option pricing. Bell. J. Econom. Management Sci. (1973) 4 141 183 Crossref, Google Scholar
• Naik V. , Uppal R. Minimum cost hedging in incomplete markets. (1992) . University of British Columbia. Working paper Google Scholar
• Rogers L. C. G. Equivalent martingale measures and no-arbitrage. Stochastics Stochastic Rep. (1994) 51 41 49 Crossref, Google Scholar
• Rubinstein M. The valuation of uncertain income streams and the pricing of options. Bell J. Econom. Management Sci. (1976) 407 425 Google Scholar
• Schachermayer W. A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time. Insurance: Math. Econom. (1992) 11 249 257 Crossref, Google Scholar
• Schäl M. , Henn R. Ein verallgemeinertes stationäres Entscheidungsmodell der dynamischen Optimierung. (1971) X 145 162 . Methods of Operations Research, Meisenheim: Anton Hain Google Scholar
• Schäl M. A selection theorem for optimization problems. Arch. Math. (1974) xxv 219 224 Crossref, Google Scholar
• Schäl M. On quadratic cost criteria for option hedging. Math. Oper. Res. (1994) 19 121 131 Link, Google Scholar
• Schäl M. An L 2-closedness property for discrete-time financial markets. (1995) . Working paper Google Scholar
• Schweizer M. Variance-optimal hedging in discrete time. Math. Oper. Res. (1995) 20 1 32 Link, Google Scholar
• Schweizer M. Approximation pricing and the variance-optimal martingale measure. Ann. Probab. (1996) 24 206 236 Crossref, Google Scholar
• Strauch R. E. Negative dynamic programming. Ann. Math. Statist. (1966) 37 871 890 Crossref, Google Scholar