Acknowledgement
This research was carried out while the first author was visiting the University of Alberta. The author is grateful to professor Tahir Choulli and other colleagues on department of mathematical and statistical sciences for their kind hosting.
References
- M. Al-Smadi, Simplified iterative reproducing kernel method for handling time-fractional BVPs with error estimation, Ain Shams Eng J. 9 (2018), 2517-2525. https://doi.org/10.1016/j.asej.2017.04.006
- N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337--404. https://doi.org/10.1090/S0002-9947-1950-0051437-7
- A. Berlinet and C. Tomas-Agnan, Reproducing kernel Hilbert spaces in probability and statistics, Springer Science, Business, Media New York, 2004.
- T. Choulli and C. Stricker, Deux application de la decomposotion de Galtchouk-Kunita-Watanabe, Seminaire De Probabilites. 30 (1996), 12--23.
- T. Choulli, J. Deng and J. Ma, How non-arbitrage, viability and numeraire portfolio are related., Finance Stoch. 19 (4) (2015), 719-741. https://doi.org/10.1007/s00780-015-0269-8
- C. Cuchiero, I. Klein and J. Teichmann, A fundamental theorem of asset pricing for continuous time large financial markets in a two filtration setting., Theory Probab. Appl. 65(3) (2020), 388-404; translation from Teor. Veroyatn. Primen. 65 (3) (2020), 498-520. https://doi.org/10.1137/S0040585X97T990022
- C. Cuchiero, I. Klein and J. Teichmann, A new perspective on the fundamental theorem of asset pricing for large financial markets., Theory Probab. Appl. 60(4) (2016), 561-579; translation from Teor. Veroyatn. Primen. 60 (4) (2015), 660-685 . https://doi.org/10.1137/S0040585X97T987879
- F. Delbaen and H. Shirakawa, A note on the no arbitrage condition for international financial markets., Financ. Eng. Jpn. Mark. 3 (3) (1994), 239-251.
- F. Delbaen and W. Schachermayer, A general version of the fundamental theorem of asset pricing., Math. Ann. 300, 33 (3) (1994), 463-520.
- F. Delbaen and W. Schachermayer, Applications to mathematical finance., Handbook of the geometry of Banach spaces. Volume 1. Amsterdam: Elsevier. 367-391 (2001).
- F. Delbaen and W. Schachermayer, Arbitrage possibilities in Bessel processes and their relations to local martingales., Probab. Theory Relat. Fields, 102 (3) (1995), 357-366. https://doi.org/10.1007/BF01192466
- F. Delbaen and W. Schachermayer, A simple counterexample to several problems in the theory of asset pricing., Math. Finance. 8 (1) (1998), 1-11. https://doi.org/10.1111/1467-9965.00041
- F. Delbaen and W. Schachermayer, The Banach space of workable contingent claims in arbitrage theory., Ann. Inst. Henri Poincare, Probab. Stat. 33 (1) (1997), 113-144. https://doi.org/10.1016/S0246-0203(97)80118-5
- F. Delbaen and W. Schachermayer, The mathematics of arbitrage., Springer Finance. Springer-Verlag, Berlin, 2006.
- C. Dellacherie, Quelques applications du lemme de Borel-Cantelli a la theeorie des semimartin-gales, Seminaire de Probabilites XII, Lecture Notes in Math., 649, 742-745, Springer, 1978.
- M. De Donno, P. Guasoni and M. Pratelli, Super-replication and utility maximization in large financial markets., Stochastic Processes Appl. 115 (12) (2005), 2006-2022. https://doi.org/10.1016/j.spa.2005.06.010
- S. Hashemi Sababe and A. Ebadian, Some properties of reproducing Kernel Banach and Hilbert spaces, Sahand commun. math. anal., 12 (1) (2018), 167-177.
- S. Hashemi Sababe, A. Ebadian and Sh. Najafzadeh, On reproducing property and 2-cocycles, Tamkang J. Math., 49 (2) (2018), 143-153. https://doi.org/10.5556/j.tkjm.49.2018.2553
- S. Hashemi Sababe, 0 On 2-inner product and reproducing property, Korean J. Math., 28 (4) (2020), 973-984. https://doi.org/10.11568/KJM.2020.28.4.973
- J. Jacod and A.N. Shiryaev, Limit theorems for stochastic processes, Springer-Verlag Berlin Heidelberg, (1987)
- Y.M. Kabanov, On the FTAP of Kreps-Delbaen-Schachermayer.,In Statistics and control of stochastic processes (Moscow,1995/1996), pages 191-203. World Sci. Publ., River Edge, NJ, 1997.
- C. Kardaras, Stochastic integration with respect to arbitrary collections of continuous semi-martingales and applications to Mathematical Finance, arXiv:1908.03946v2 [math.PR], 2019.
- H. Kunita and Sh. Watanabe On square integrable martingales, Nagoya Math. J. 30 (1967), 209-245. https://projecteuclid.org/euclid.nmj/1118796812 https://doi.org/10.1017/S0027763000012484
- R. Mikulevicius and B.L. Rozovskii, Normalized stochastic integrals in topological vector spaces, Seminaire de Probabilites XXXII, Lecture Notes in Math., Springer, 137-165, Springer, 1998.
- R. Mikulevicius and B.L. Rozovskii, Martingale problems for stochastic PDE's, Amer. Math. Soc., 64 (1999), 243-326,
- J. Memin, Espaces de semi martingales et changement de probabilite, Z Wahrscheinlichkeit 52 (1980), 9-39. https://doi.org/10.1007/BF00534184
- M. Schuld and N. Killoran, Quantum Machine Learning in Feature Hilbert Spaces, Phys Rev Lett, 122 (2018), 040504(1)-040504(6). https://doi.org/10.1103/physrevlett.122.040504
- S. Vahdati, M. Fardi and M. Ghasemi, Option pricing using a computational method based on reproducing kernel, J Comput Appl Math, 328 (2018), 252-266. https://doi.org/10.1016/j.cam.2017.05.032