Rate of convergence of approximations of some convex functionals of stochastic differential equations

Henri Schurz

doi:10.1117/12.619474

23 May 2005 Rate of convergence of approximations of some convex functionals of stochastic differential equations

Henri Schurz

Proceedings Volume 5848, Noise and Fluctuations in Econophysics and Finance; (2005) https://doi.org/10.1117/12.619474
Event: SPIE Third International Symposium on Fluctuations and Noise, 2005, Austin, Texas, United States

Abstract

The rate of convergence of numerical methods for integration of some convex 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 non-smooth and convex functionals of SDEs. Qualitative behavior of some numerical approximations such as nonnegativity of balanced implicit Milstein methods (BMMs) is investigated as well. Nonstandard integration techniques such as partial- and linear-implicit ones seem to be the most promissing. As a main result we obtain some justification for the choice of approximation schemes of discounted price functionals and their ingredients of random interest rates and volatility processes involved in dynamic asset pricing.

Citation Download Citation

Henri Schurz "Rate of convergence of approximations of some convex functionals of stochastic differential equations", Proc. SPIE 5848, Noise and Fluctuations in Econophysics and Finance, (23 May 2005); https://doi.org/10.1117/12.619474

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available