TY - JOUR
T1 - How Rates of L^{p}-Convergence Carry Over to Numerical Approximations of Some Convex Non-Smooth Functionals of SDES
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 55
EP - 72
PY - 2008
DA - 2008/05
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/797.html
KW - stochastic differential equations
KW - approximation of convex and path-dependent functionals
KW - numerical methods
KW - stability
KW - L-P-convergence
KW - weak convergence
KW - rates of convergence
KW - non-negativity
KW - discounted price functionals
KW - asset pricing
KW - approximation of
AB - The relation between weak and p-th mean convergence of
numerical methods for integration of some convex, non-smooth and
path-dependent functionals of ordinary stochastic differential equations
(SDEs) is discussed. In particular, we answer how rates of p-th mean
convergence carry over to rates of weak convergence for such functionals
of SDEs in general. Assertions of this type are important for the choice
of approximation schemes for discounted price functionals in dynamic
asset pricing as met in mathematical finance and other commonly met
functionals such as passage times in engineering.