TY - JOUR
T1 - On the space discretization of pdes with unbounded coefficients arising in financial mathematics. a case of one spatial dimension
AU - Gonçalves, Fernando F.
AU - Grossinho, Maria do Rosario
AU - Morais, Eva
PY - 2010
Y1 - 2010
N2 - We study the space discretization of the Cauchy problem for a second order linear parabolic PDE, with one spatial dimension and unbounded time and space-dependent coefficients. The PDE free term and the initial data are also allowed to grow. Under the assumption that the PDE does not degenerate, the problem's weak solution is approximated in space, with finite-difference methods. The rate of convergence is estimated. A numerical example is given in order to illustrate the theoretical results.
AB - We study the space discretization of the Cauchy problem for a second order linear parabolic PDE, with one spatial dimension and unbounded time and space-dependent coefficients. The PDE free term and the initial data are also allowed to grow. Under the assumption that the PDE does not degenerate, the problem's weak solution is approximated in space, with finite-difference methods. The rate of convergence is estimated. A numerical example is given in order to illustrate the theoretical results.
KW - Cauchy problem
KW - Finite-difference method
KW - Option pricing
KW - Parabolic partial differential equations
KW - Un-bounded coefficients
UR - http://www.scopus.com/inward/record.url?scp=76749101629&partnerID=8YFLogxK
M3 - Article
SN - 1310-1331
VL - 63
SP - 35
EP - 46
JO - Comptes Rendus de L'Academie Bulgare des Sciences
JF - Comptes Rendus de L'Academie Bulgare des Sciences
IS - 1
ER -