On‐Line Portfolio Selection Using Multiplicative Updates

@article{Helmbold1996OnLinePS,
  title={On‐Line Portfolio Selection Using Multiplicative Updates},
  author={David P. Helmbold and Robert E. Schapire and Yoram Singer and Manfred K. Warmuth},
  journal={Mathematical Finance},
  year={1996},
  volume={8}
}
We present an on‐line investment algorithm that achieves almost the same wealth as the best constant‐rebalanced portfolio determined in hindsight from the actual market outcomes. The algorithm employs a multiplicative update rule derived using a framework introduced by Kivinen and Warmuth. Our algorithm is very simple to implement and requires only constant storage and computing time per stock in each trading period. We tested the performance of our algorithm on real stock data from the New… 
An Additive On-Line Portfolio Selection Algorithm
TLDR
An on-line portfolio management algorithm using additive update rule is presented with consideration of proportional transaction costs and it is shown that the presented portfolio strategy is universal relative to the set of all buy-and-hold portfolios in the sense that it achieves the same asymptotic exponential growth rate of wealth.
A class of on-line portfolio selection algorithms based on linear learning
Algorithms for portfolio management based on the Newton method
TLDR
Experiments confirm the theoretical advantage of the algorithms, which yield higher returns and run considerably faster than previous algorithms with optimal regret, which are the first to combine optimal logarithmic regret bounds with efficient deterministic computability.
Risk-Adjusted On-line Portfolio Selection
TLDR
This work presents a novel risk-adjusted portfolio selection algorithm (RAPS), which incorporates the ‘trading risk’ in terms of the maximum possible loss and shows that RAPS performs provably ‘as well as’ the Universal Portfolio (UP) in the worst-case.
Switching Portfolios
  • Y. Singer
  • Economics, Computer Science
    Int. J. Neural Syst.
  • 1997
TLDR
This paper presents an efficient portfolio selection algorithm that is able to track a changing market and provides a simple analysis of the competitiveness of the algorithm and check its performance on real stock data from the New York Stock Exchange accumulated during a 22-year period.
Portfolio Selection and Online Learning
  • T. Levina, G. Shafer
  • Computer Science, Economics
    Int. J. Uncertain. Fuzziness Knowl. Based Syst.
  • 2008
TLDR
The proposed investment strategy achieves asymptotically the same exponential rate of growth as the portfolio that turns out to be best expost in the long run and does not require any underlying statistical assumptions on the nature of the stock market.
Online Portfolio Optimization with Exponential Gradient and Time Varying CAPM
TLDR
The purpose of this paper was to implement a new version of the Exponential Gradient algorithm in which important information about the risk of stocks are considered in the algorithm’s projection step, and the EG beta algorithm outperformed the DJIA in all tests performed.
Online Lazy Updates for Portfolio Selection with Transaction Costs
TLDR
An efficient primal-dual based online algorithm that performs lazy updates to the parameter vector and shows that its performance is competitive with reasonable strategies which have the benefit of hindsight.
Universal switching portfolios under transaction costs
  • S. Kozat, A. Singer
  • Computer Science
    2008 IEEE International Conference on Acoustics, Speech and Signal Processing
  • 2008
TLDR
A sequential algorithm for portfolio selection that asymptotically achieves the wealth of the best piecewise constant rebalanced portfolio tuned to the underlying individual sequence of price relative vectors where the authors pay a fixed percent commission for each transaction.
Growth optimal investment with threshold rebalancing portfolios under transaction costs
TLDR
A portfolio selection algorithm is introduced that maximizes the expected cumulative wealth in i.i.d. two-asset discrete-time markets where the market levies proportional transaction costs in buying and selling stocks.
...
...

References

SHOWING 1-10 OF 46 REFERENCES
Switching Portfolios
  • Y. Singer
  • Economics, Computer Science
    Int. J. Neural Syst.
  • 1997
TLDR
This paper presents an efficient portfolio selection algorithm that is able to track a changing market and provides a simple analysis of the competitiveness of the algorithm and check its performance on real stock data from the New York Stock Exchange accumulated during a 22-year period.
Empirical Bayes stock market portfolios
Universal portfolios with side information
TLDR
This is an individual sequence result which shows the difference between the exponential growth wealth of the best state-constant rebalanced portfolio and the universal portfolio with side information is uniformly less than (d/(2n))log (n+1)+(k/n)log 2 for every stock market and side-information sequence and for all time n.
Asymptotic optimality and asymptotic equipartition properties of log-optimum investment
We ask how an investor (with knowledge of the past) should distribute his funds over various investment opportunities to maximize the growth rate of his compounded capital. Breiman (1961) answered
Universal Portfolios
We exhibit an algorithm for portfolio selection that asymptotically outperforms the best stock in the market. Let x i = (x i1 ; x i2 ; : : : ; x im) t denote the performance of the stock market on
Competitive Optimality of Logarithmic Investment
TLDR
The immediate goal of outperforming another investor is perfectly compatible with maximizing the asymptotic rate of return, which achieves the maximum possible growth rate of capital in repeated independent investments.
Options, Futures, and Other Derivatives
Contents: Introduction. Futures Markets and the Use of Futures for Hedging. Forward and Futures Prices. Interest Rate Futures. Swaps. Options Markets. Properties of Stock Option Prices. Trading
A bound on the financial value of information
TLDR
The bound is shown to be a special case of the result that the increase in exponential growth of wealth achieved with true knowledge of the stock market distribution F over that achieved with incorrect knowledge G is bounded above by the entropy of F relative to G.
Game-theoretic optimal portfolios
We show, for a wide variety of payoff functions, that the expected log optimal portfolio is also game theoretically optimal in a single play or in multiple plays of the stock market. Thus there is no
Additive versus exponentiated gradient updates for linear prediction
TLDR
The main methodological idea is using a distance function between weight vectors both in motivating the algorithms and as a potential function in an amortized analysis that leads to worst-case loss bounds.
...
...