TY - JOUR
T1 - How Rates of $L^p$-Convergence Carry over to Numerical Approximations of Some Convex, Non-Smooth Functionals of SDEs
AU - Schurz , Henri
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, approximation of convex and path-dependent functionals, numerical methods, stability, $L^p$-convergence, weak convergence, rates of convergence, non-negativity, discounted price functionals, asset pricing, approximation of stochastic exponentials.
AB - <p style="text-align: justify;">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.</p>