On Universal Portfolios with Continuous Side Information
Alankrita Bhatt, J. Jon Ryu, Young-Han Kim
Abstract
A new portfolio selection strategy that adapts to a continuous side-information sequence is presented, with a universal wealth guarantee against a class of state-constant rebalanced portfolios with respect to a state function that maps each side-information symbol to a finite set of states. In particular, given that a state function belongs to a collection of functions of finite Natarajan dimension, the proposed strategy is shown to achieve, asymptotically to first order in the exponent, the same wealth as the best state-constant rebalanced portfolio with respect to the best state function, chosen in hindsight from observed market. This result can be viewed as an extension of the seminal work of Cover and Ordentlich (1996) that assumes a single-state function.
BibTeX
@InProceedings{pmlr-v206-bhatt23a,
title = {On Universal Portfolios with Continuous Side Information},
author = {Bhatt, Alankrita and Ryu, J. Jon and Kim, Young-Han},
booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics},
pages = {4147--4163},
year = {2023},
editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem},
volume = {206},
series = {Proceedings of Machine Learning Research},
month = {25--27 Apr},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v206/bhatt23a/bhatt23a.pdf},
url = {https://proceedings.mlr.press/v206/bhatt23a.html},
abstract = {A new portfolio selection strategy that adapts to a continuous side-information sequence is presented, with a universal wealth guarantee against a class of state-constant rebalanced portfolios with respect to a state function that maps each side-information symbol to a finite set of states. In particular, given that a state function belongs to a collection of functions of finite Natarajan dimension, the proposed strategy is shown to achieve, asymptotically to first order in the exponent, the same wealth as the best state-constant rebalanced portfolio with respect to the best state function, chosen in hindsight from observed market. This result can be viewed as an extension of the seminal work of Cover and Ordentlich (1996) that assumes a single-state function.}
}