# Universal Portfolios

@inproceedings{Cover1996UniversalP, title={Universal Portfolios}, author={Thomas M. Cover}, year={1996} }

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 day i ; where x ij is the factor by which the j-th stock increases on day i : Let b i = (b i1 ; b i2 ; : : : ; b im) t ; b ij 0; P j b ij = 1 ; denote the proportion b ij of wealth invested in the j-th stock on day i : Then S n = Q n i=1 b t i x i is the factor by which wealth is increased in n…

## 528 Citations

An Introduction To Regret Minimization In Algorithmic Trading: A Survey of Universal Portfolio Techniques

- EconomicsArXiv
- 2021

To make this question more precise, let’s introduce some notation. For i ∈ [1, T ], let xi ∈ R+ denote the price relative vector between days i − 1 and i. In particular, this means that (xi)j :=…

Universal Portfolios With and Without Transaction Costs

- Economics
- 2008

Suppose that there are m stocks in a market, which we are interested in investing in over n days. On each day an investor will picks a way to distribute her money in the market. Let b ∈ R be a vector…

Switching Portfolios

- Economics, Computer ScienceInt. J. Neural Syst.
- 1997

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.

Optimal Investment Under Transaction Costs

- Economics
- 2012

This work constructs portfolios that achieve the optimal expected growth in i.i.d. discrete-time two-asset markets under proportional transaction costs and evaluates the corresponding stationary distribution of this Markov chain, which provides a natural and efficient method to calculate the cumulative expected wealth.

AN ONLINE PORTFOLIO SELECTION ALGORITHM WITH REGRET LOGARITHMIC IN PRICE VARIATION

- Computer Science
- 2014

It is proved that the regret of the algorithm is bounded by O(log Q), where Q is the quadratic variation of the stock prices, and this is the first improvement upon Cover's (1991) seminal work that attains a regret bound of O( log T), where T is the number of trading iterations.

Optimal Investment Under Transaction Costs: A Threshold Rebalanced Portfolio Approach

- EconomicsIEEE Transactions on Signal Processing
- 2013

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.

Robust Asset Allocation with Benchmarked Objectives

- Economics, Computer Science
- 2008

In this paper, we introduce a new approach for finding robust portfolios when there is model uncertainty. It differs from the usual worst case approach in that a (dynamic) portfolio is evaluated not…

Online Portfolio Optimization with Risk Control

- Computer ScienceTrends in Computational and Applied Mathematics
- 2021

This work compared the performance of the traditional OGD algorithm and the OGD with Beta constraints with the Uniform Constant Rebalanced Portfolio and two different indexes for the Brazilian market, composed of small caps and the assets that belong to the Ibovespa index.

Cooperative Multiagent Search for Portfolio

- Economics
- 2007

We present a new multiagent model for the multi-period portfolio selection problem. Individual agents receive a share of initial wealth, and follow an investment strategy that adjusts their portfolio…

The Cost of Achieving the Best Portfolio in Hindsight

- EconomicsMath. Oper. Res.
- 1998

The optimal ratio Vn is shown to decrease only polynomially in n, indicating that the rate of return of the optimal strategy converges uniformly to that of the best constant rebalanced portfolio determined with full hindsight.

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