Browse > Article
http://dx.doi.org/10.11568/kjm.2021.29.3.639

REPRODUCING KERNEL HILBERT SPACE BASED ON SPECIAL INTEGRABLE SEMIMARTINGALES AND STOCHASTIC INTEGRATION  

Sababe, Saeed Hashemi (Young Researchers and Elite Club, Malard Branch, Islamic Azad University)
Yazdi, Maryam (Young Researchers and Elite Club, Malard Branch, Islamic Azad University)
Shabani, Mohammad Mehdi (Faculty of sciences, Imam Ali University)
Publication Information
Korean Journal of Mathematics / v.29, no.3, 2021 , pp. 639-647 More about this Journal
Abstract
In this paper, we consider the integral of a stochastic process with respect of a sequence of square integrable semimartingales. By this integrals, we construct a reproducing kernel Hilbert space and study the correspondence between this space with the concepts of arbitrage and viability in mathematical finance.
Keywords
stochastic integration; continuous semimartingales; reproducing kernels;
Citations & Related Records
연도 인용수 순위
  • Reference
1 J. Jacod and A.N. Shiryaev, Limit theorems for stochastic processes, Springer-Verlag Berlin Heidelberg, (1987)
2 C. Kardaras, Stochastic integration with respect to arbitrary collections of continuous semi-martingales and applications to Mathematical Finance, arXiv:1908.03946v2 [math.PR], 2019.
3 H. Kunita and Sh. Watanabe On square integrable martingales, Nagoya Math. J. 30 (1967), 209-245. https://projecteuclid.org/euclid.nmj/1118796812   DOI
4 R. Mikulevicius and B.L. Rozovskii, Martingale problems for stochastic PDE's, Amer. Math. Soc., 64 (1999), 243-326,
5 J. Memin, Espaces de semi martingales et changement de probabilite, Z Wahrscheinlichkeit 52 (1980), 9-39.   DOI
6 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.   DOI
7 T. Choulli and C. Stricker, Deux application de la decomposotion de Galtchouk-Kunita-Watanabe, Seminaire De Probabilites. 30 (1996), 12--23.
8 T. Choulli, J. Deng and J. Ma, How non-arbitrage, viability and numeraire portfolio are related., Finance Stoch. 19 (4) (2015), 719-741.   DOI
9 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.   DOI
10 F. Delbaen and W. Schachermayer, A general version of the fundamental theorem of asset pricing., Math. Ann. 300, 33 (3) (1994), 463-520.
11 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.
12 A. Berlinet and C. Tomas-Agnan, Reproducing kernel Hilbert spaces in probability and statistics, Springer Science, Business, Media New York, 2004.
13 S. Hashemi Sababe, A. Ebadian and Sh. Najafzadeh, On reproducing property and 2-cocycles, Tamkang J. Math., 49 (2) (2018), 143-153.   DOI
14 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.
15 M. Schuld and N. Killoran, Quantum Machine Learning in Feature Hilbert Spaces, Phys Rev Lett, 122 (2018), 040504(1)-040504(6).   DOI
16 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.
17 F. Delbaen and W. Schachermayer, A simple counterexample to several problems in the theory of asset pricing., Math. Finance. 8 (1) (1998), 1-11.   DOI
18 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.   DOI
19 M. Al-Smadi, Simplified iterative reproducing kernel method for handling time-fractional BVPs with error estimation, Ain Shams Eng J. 9 (2018), 2517-2525.   DOI
20 N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337--404.   DOI
21 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.   DOI
22 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.
23 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 .   DOI
24 F. Delbaen and W. Schachermayer, Applications to mathematical finance., Handbook of the geometry of Banach spaces. Volume 1. Amsterdam: Elsevier. 367-391 (2001).
25 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.   DOI
26 F. Delbaen and W. Schachermayer, The mathematics of arbitrage., Springer Finance. Springer-Verlag, Berlin, 2006.
27 S. Hashemi Sababe and A. Ebadian, Some properties of reproducing Kernel Banach and Hilbert spaces, Sahand commun. math. anal., 12 (1) (2018), 167-177.
28 S. Hashemi Sababe, 0 On 2-inner product and reproducing property, Korean J. Math., 28 (4) (2020), 973-984.   DOI