Download this PDF file Fullscreen Fullscreen Off
References
- Ansel, Jean-Pascal and Stricker, Christophe. Lois de martingale, densités et décomposition de Föllmer-Schweizer. (French) [Martingale laws, densities and Follmer-Schweizer decomposition] Ann. Inst. H. Poincaré Probab. Statist. 28 (1992), no. 3, 375--392. MR1183992 (94d:60069)
- Back, Kerry; Pliska, Stanley R. On the fundamental theorem of asset pricing with an infinite state space. J. Math. Econom. 20 (1991), no. 1, 1--18. MR1068218 (91d:90007)
- Bättig, Robert. Completeness of securities market models---an operator point of view. Ann. Appl. Probab. 9 (1999), no. 2, 529--566. MR1687390 (2000m:91063)
- Bättig, Robert
and Jarrow, R. J.: The Second
Fundamental Theorem of Asset Pricing: A New Approach,
The Review of Financial Studies, 12(5)
(1999), 1219--1235.
- Bensoussan, A. On the theory of option pricing. Acta Appl. Math. 2 (1984), no. 2, 139--158. MR0748007 (86j:90027)
- Boyle, Phelim and Broadie, Mark; Glasserman, Paul. Monte Carlo methods for security pricing. Computational financial modelling. J. Econom. Dynam. Control 21 (1997), no. 8-9, 1267--1321. MR1470283
- Broadie, M. and Detemple, J. : American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods, The Review of Financial Studies, 9(4) (1996), 1211--1250.
- Carverhill, A. P. and Webber, N.: American Options: Theory and Numerical Analysis, Options: Recent Advances in Theory and Practice. Manchester University Press, 1990.
- Clark, Stephen A. The valuation problem in arbitrage price theory. J. Math. Econom. 22 (1993), no. 5, 463--478. MR1231237 (94g:90012)
- Delbaen, F.: Representing Martingale Measures When Asset Prices are Continuous and Bounded, Mathematical Finance, 2 (1992), 107--130.
- Delbaen, Freddy and Schachermayer, Walter. A general version of the fundamental theorem of asset pricing. Math. Ann. 300 (1994), no. 3, 463--520. MR1304434 (95m:90022b)
- Delbaen, F. and Schachermayer, W. Arbitrage possibilities in Bessel processes and their relations to local martingales. Probab. Theory Related Fields 102 (1995), no. 3, 357--366. MR1339738 (97b:90018)
- Delbaen, Freddy and Schachermayer, Walter. The existence of absolutely continuous local martingale measures. Ann. Appl. Probab. 5 (1995), no. 4, 926--945. MR1384360 (97g:60059)
- Delbaen, F. and Schachermayer, W. Attainable claims with $p$th moments. Ann. Inst. H. Poincaré Probab. Statist. 32 (1996), no. 6, 743--763. MR1422309 (98c:90012)
- Delbaen, Freddy and Schachermayer, Walter. The Banach space of workable contingent claims in arbitrage theory. Ann. Inst. H. Poincaré Probab. Statist. 33 (1997), no. 1, 113--144. MR1440258 (98f:60105)
- Delbaen, Freddy and Schachermayer, Walter. ``The Fundamental Theorem of Asset Pricing for Unbounded Stochastic Processes,'' Mimeo. Institut für Statistik der Unversität Wien. 1997.
- Delbaen, Freddy and Schachermayer, Walter. ``Non-Arbitrage and the Fundamental Theorem of Asset Pricing: Summary of Main Results,'' Proceedings of Symposia in Applied Mathematics, 00 (1997), 1--10.
- Delbaen, Freddy and Schachermayer, Walter. A simple counterexample to several problems in the theory of asset pricing. Math. Finance 8 (1998), no. 1, 1--11. MR1613358 (99i:90014)
- Duffie, D. Dynamic Asset Pricing Theory . Princeton University Press, Princeton, New Jersey, second edn.
- Duffie, Darrell and Huang, Chi-fu. Multiperiod security markets with differential information: martingales and resolution times. J. Math. Econom. 15 (1986), no. 3, 283--303. MR0871158 (88b:90045)
- Dybvig, P. H. and Huang, C. Nonnegative Wealth, Absence of Arbitrage and Feasible Consumption Plans,
The Review of Financial Studies, 1(4) (1988), 377--401.- Fernholz, R., Karatzas I. and Kardaras, C. (2004): Diversity and arbitrage in financial markets Finance & Stochastics (to appear), 2004.
- Harrison, J. Michael and Kreps, David M. Martingales and arbitrage in multiperiod securities markets. J. Econom. Theory 20 (1979), no. 3, 381--408. MR0540823 (80h:90025)
- Harrison, J. Michael and Pliska, Stanley R. Martingales and stochastic integrals in the theory of continuous trading. Stochastic Process. Appl. 11 (1981), no. 3, 215--260. MR0622165 (83a:90022)
- Harrison, J. Michael; Pliska, Stanley R. A stochastic calculus model of continuous trading: complete markets. Stochastic Process. Appl. 15 (1983), no. 3, 313--316. MR0711188 (84m:90016)
- Hindy, Ayman. Viable prices in financial markets with solvency constraints. J. Math. Econom. 24 (1995), no. 2, 105--135. MR1316976 (96f:90026)
- Hull, J. Options, Futures, and Other Derivative Securities. Prentice-Hall, Englewood Cliffs, second edn. 1993.
- Jarrow, R. and Madan, D. B. A Characterization of Complete Security Markets on A Brownian Filtration, Mathematical Finance, 1(3) (1991), 31--44.
- Jarrow, Robert and Madan, Dilip B. Hedging contingent claims on semimartingales. Finance Stoch. 3 (1999), no. 1, 111--134. MR1805323 (2002c:91064)
- Karatzas, Ioannis. On the pricing of American options. Appl. Math. Optim. 17 (1988), no. 1, 37--60. MR0908938 (88j:90026)
- Karatzas, Ioannis. Lectures on the mathematics of finance. CRM Monograph Series, 8. American Mathematical Society, Providence, RI, 1997. xii+148 pp. ISBN: 0-8218-0637-8 MR1421066 (98h:90001)
- Karatzas, Ioannis; Shreve, Steven E. Methods of mathematical finance. Applications of Mathematics (New York), 39. Springer-Verlag, New York, 1998. xvi+407 pp. ISBN: 0-387-94839-2 MR1640352 (2000e:91076)
- Kreps, David M. Arbitrage and equilibrium in economies with infinitely many commodities. J. Math. Econom. 8 (1981), no. 1, 15--35. MR0611252 (82m:90038)
- Lakner, P. Martingale Measures for a class of right-continuous Processes, Mathematical Finance, 3 ((1993), 43--53.
- Levental, Shlomo; Skorohod, Anatolii V. A necessary and sufficient condition for absence of arbitrage with tame portfolios. Ann. Appl. Probab. 5 (1995), no. 4, 906--925. MR1384359 (98c:90014)
- Loewenstein, Mark; Willard, Gregory A. Local martingales, arbitrage, and viability. Free snacks and cheap thrills. Econom. Theory 16 (2000), no. 1, 135--161. MR1774056 (2001d:91100)
- Myneni, Ravi. The pricing of the American option. Ann. Appl. Probab. 2 (1992), no. 1, 1--23. MR1143390 (92h:90018)
- Schachermayer, W. Martingale measures for discrete-time processes with infinite horizon. Math. Finance 4 (1994), no. 1, 25--55. MR1286705 (95m:90022a)
- Schweizer, Martin. Martingale densities for general asset prices. J. Math. Econom. 21 (1992), no. 4, 363--378. MR1164787 (93h:90012)
- Stricker, Christophe. Arbitrage et lois de martingale. (French) [Arbitrage and martingale laws] Ann. Inst. H. Poincaré Probab. Statist. 26 (1990), no. 3, 451--460. MR1066088 (91m:60080)
- Willard, G. A. and Dybvig, P. H. : Empty Promises and Arbitrage, The Review of Financial Studies, 12(4) (1999), 807--834.
- Wilmott, P., Dewynne, J. and Howison, S.: Option Pricing: Mathematical Models and Computation. Oxford Financial Press, Oxford, 1993.

This work is licensed under a Creative Commons Attribution 3.0 License.