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Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 12
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Original Articles

Iterative scheme for an elliptic non-local free boundary problem

R. BarkhudaryanInstitute of Mathematics, Yerevan, Armenia.Correspondence[email protected]
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,
M. JurášDepartment of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar.View further author information
&
M. SalehiDepartment of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar.View further author information
Pages 2794-2806 | Received 23 Jul 2015, Accepted 24 Oct 2015, Published online: 20 Nov 2015

References

  • Scheinkman JA, Xiong W. Overconfidence and speculative bubbles. J. Polit. Econ. 2003;111:1183–1220.
  • Chen X, Kohn RV. Erratum to: asset price bubbles from heterogeneous beliefs about mean reversion rates [mr2800215]. Finance Stoch. 2013;17:225–226.
  • Chen X, Kohn RV. Asset price bubbles from heterogeneous beliefs about mean reversion rates. Finance Stoch. 2011;15:221–241.
  • Berestycki H, Monneau R, Scheinkman JA. A non-local free boundary problem arising in a theory of financial bubbles. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 2014;372:20130404, 36.
  • Caffarelli LA. The obstacle problem revisited. J. Fourier Anal. Appl. 1998;4:383–402.
  • Petrosyan A, Shahgholian H, Uraltseva N. Regularity of free boundaries in obstacle-type problems. Vol. 136, Graduate Studies in Mathematics. Providence (RI): American Mathematical Society; 2012.
  • Burger M, Caffarelli L, Markowich PA. Partial differential equation models in the socio-economic sciences. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 2014;372:20130406, 8.
  • Crandall MG, Lions P-L. Viscosity solutions of Hamilton--Jacobi equations. Trans. Am. Math. Soc. 1982;277:1–42.
  • Crandall MG, Evans LC, Lions P-L. Some properties of viscosity solutions of Hamilton--Jacobi equations. Trans. Am. Math. Soc. 1984;282:487–502.
  • Crandall MG, Ishii H, Lions P-L. User’s guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. (N.S.). 1992;27:1–67.
  • Caffarelli LA, Cabr\’{e} X. Fully nonlinear elliptic equations. Vol. 43, American Mathematical Society Colloquium Publications. Providence (RI): American Mathematical Society; 1995.
  • Friedman A. Variational principles and free-boundary problems. Pure and Applied Mathematics. New York (NY): Wiley; 1982. A Wiley-Interscience Publication.
  • Andersson J, Shahgholian H, Weiss GS. Double obstacle problems with obstacles given by non-C2 Hamilton--Jacobi equations. Arch. Ration. Mech. Anal. 2012;206:779–819.
  • Reppen M, Moosavi P. A review of the double obstacle problem. Master’s thesis, Stockholm: KTH Royal Institute of Technology; 2011.
  • Olek A, Szczepaniak K. Continuous dependence on obstacles in double global obstacle problems. Ann. Acad. Sci. Fenn. Math. 2003;28:89–97.
  • Dai M, Yi F. Finite-horizon optimal investment with transaction costs: a parabolic double obstacle problem. J. Differ. Equ. 2009;246:1445–1469.
  • Wilmott P, Dewynne J, Howison S. Option pricing: mathematical models and computation. Oxford Financial Press; Oxford, 1993.
  • Hu B, Liang J, Jiang L. Optimal convergence rate of the explicit finite difference scheme for American option valuation. J. Comput. Appl. Math. 2009;230:583–599.
  • Arakelyan AG, Barkhudaryan RH, Poghosyan MP. Finite difference scheme for two-phase obstacle problem. Dokl. Nats. Akad. Nauk Armen. 2011;111:224–231.
  • Arakelyan A, Barkhudaryan R, Pogosyan M. An error estimate for the finite difference method for the one-phase obstacle problem. Izv. Nats. Akad. Nauk Armenii Mat. 2011;46:3–16.
  • Arakelyan A. A finite difference method for two-phase parabolic obstacle-like problem. Armen. J. Math. 2015;7:32–49.

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