Volume 5, Issue 1
How Rates of Lp-Convergence Carry Over to Numerical Approximations of Some Convex Non-Smooth Functionals of SDES

R. K. Mohanty & S. Singh

Int. J. Numer. Anal. Mod., 5 (2008), pp. 55-72.

Published online: 2008-05

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  • Abstract

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.

  • Keywords

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

  • AMS Subject Headings

65C30 65L20 65D30 34F05 37H10 60H10

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-5-55, author = {}, title = {How Rates of Lp-Convergence Carry Over to Numerical Approximations of Some Convex Non-Smooth Functionals of SDES}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2008}, volume = {5}, number = {1}, pages = {55--72}, abstract = {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. }, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/797.html} }
TY - JOUR T1 - How Rates of Lp-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.
R. K. Mohanty & S. Singh. (2019). How Rates of Lp-Convergence Carry Over to Numerical Approximations of Some Convex Non-Smooth Functionals of SDES. International Journal of Numerical Analysis and Modeling. 5 (1). 55-72. doi:
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