Arbitrage and approximate arbitrage: the fundamental theorem of asset pricing

References

• Battig , R. and Jarrow , R. 1999 . The second fundamental theorem of asset pricing: A new approach . Rev. Finac. Stud. , 12 : 1219 – 1235 .
   Google Scholar
• Clark , S. 2000 . Arbitrage approximation theory . J. Math. Econom. , 33 : 167 – 181 .
   Google Scholar
• Dalang , R. , Morton , A. and Willinger , W. 1990 . Equivalent martingale measures and no-arbitrage in stochastic securities markets models . Stoch. Stoch. Rep. , 29 : 185 – 201 .
   Google Scholar
• Delbaen , F. and Schachermayer , W. 1993 . No Arbitrage and the fundamental theorem of asset pricing , Abstract Book of the SPA Meeting 37 – 38 . Amsterdam June
   Google Scholar
• Delbaen , F. and Schachermayer , W. 1994 . Arbitrage and free lunch with bounded risk in unbounded continuous processes . Math. Finance , 4 : 343 – 348 .
   Google Scholar
• Delbaen , F. and Schachermayer , W. 1994 . A general version of the fundamental theorem of asset pricing . Math. Ann. , 300 : 464 – 520 .
   Google Scholar
• Delbaen , F. and Schachermayer , W. 1995 . The existence of absolutely continuous local martingale measures . Ann. Appl. Probab. , 5 : 926 – 945 .
   Google Scholar
• Delbaen , F. and Schachermayer , W. 1999 . No-arbitrage and the fundamental theorem of asset pricing: Summary of main results . Proc. Symp. Appl. Math. , 57 : 49 – 58 .
   Google Scholar
• Duffie , D. 2002 . Dynamic Asset Pricing Theory , 3rd ed. , Princeton, NJ : Princeton University Press .
   Google Scholar
• Dybvig , P. and Huang , C. 1998 . Nonnegative wealth, absence of arbitrage, and feasible consumption plans . Rev. Finac. Stud. , 1 : 377 – 401 .
   Google Scholar
• Elliott , R. 1982 . Stochastic Calculus and Applications , New York, NY : Springer-Verlag .
   Google Scholar
• Elworthy , K. , Li , X.-M. and Yor , M. 1999 . The importance of strictly local martingales; applications to radial Ornstein Uhlenbeck processes . Probab. Theory Relat. Fields , 115 : 325 – 355 .
   Google Scholar
• Harrison , M. and Kreps , D. 1979 . Martingales and arbitrage in multiperiod securities markets . J. Econom. Theory , 20 : 381 – 408 .
   Google Scholar
• Harrison , M. and Pliska , S. 1981 . Martingales and stochastic integrals in the theory of continuous trading . Stochastic Process. Appl. , 11 : 215 – 260 .
   Google Scholar
• Jouini , E. 2001 . Arbitrage and control problems in finance: A presentation . J. Math. Econom. , 35 : 167 – 183 .
   Google Scholar
• Kabanov , Y. 2001 . “ Arbitrage theory ” . In Option Pricing, Interest Rates and Risk Management , Edited by: Jouini , Cvitanic and Musiela . 3 – 42 . Cambridge : Cambridge University Press .
   Google Scholar
• Kabanov , Y. and Stricker , C. 2005 . Remarks on the No-arbitrage Property , Seminaire de Probabilites XXXVIII, Lecture Notes in Mathematics, 1857 Berlin : Springer-Verlag .
   Google Scholar
• Karatzas , I. and Shreve , S. 1991 . Brownian Motion and Stochastic Calculus , 2nd ed. , New York, NY : Springer-Verlag .
   Google Scholar
• Karatzas , I. and Shreve , S. 1998 . Methods of Mathematical Finance , New York, NY : Springer-Verlag .
   Google Scholar
• Karatzas , I. , Lehoczky , J. , Shreve , S. and Xu , G. 1991 . Martingale and duality methods for utility maximization in incomplete markets . SIAM J. Control Optim. , 29 : 702 – 730 .
   Google Scholar
• Kazamaki , N. 1994 . Continuous Exponential Martingales and BMO , Lecture Notes in Mathematics, 1579 Berlin : Springer-Verlag .
   Google Scholar
• Levental , S. and Skorohod , A. 1995 . A necessary and sufficient condition for absence of arbitrage with tame portfolios . Ann. Appl. Probab. , 5 : 906 – 992 .
   Google Scholar
• Loweinstein , M. and Williard , G. 2000 . Local martingales, arbitrage, and viability: Free snacks and cheap thrills . Econom. Theory , 16 : 135 – 161 .
   Google Scholar
• Protter , P. 2004 . Stochastic Integration and Differential Equations , 2nd ed. , Berlin : Springer-Verlag .
   Google Scholar
• Revuz , D. and Yor , M. 2001 . Continuous Martingales and Brownian Motion , 3rd ed. , Berlin : Springer-Verlag . (corrected second printing)
   Google Scholar