Abstract
An inequality involving the Kullback-Leibler and chi-square divergences is used to generate new universal portfolios for investment. The stationary vector of an objective function is determined for the purpose of deciding the next-day portfolio given the current-day portfolio and the current-day price relative vector. The two-parameter portfolio is studied empirically by running the portfolio on selected stock-price data sets from the local stock exchange. It is demonstrated that the wealth of the investor can be increased by using the proposed universal portfolio.
Highlights
Daniel Bernoulli’s article about log utility and the St
Universal portfolios weighted by moments of probability distribution is proposed in [14]
Another method of deriving universal portfolios using the stationary vector of an objective function is initiated by Helmbold et al [15]
Summary
Daniel Bernoulli’s article about log utility and the St. Petersburg Paradox was written in 1738. Bell and Cover demonstrated that a game theoretically optimal portfolio is possible by maximizing the conditional expected log return [8]. Given information of the historical data, Algoet and Cover proved that the conditional expected log return can be maximized [11]. Universal portfolios weighted by moments of probability distribution is proposed in [14] Another method of deriving universal portfolios using the stationary vector of an objective function is initiated by Helmbold et al [15]. This method is generalized by Tan and Lee [16] to generate universal portfolios from the CauchySchwarz and Hölder inequalities. Universal portfolios generated from the f and Bregman divergences are discussed in Tan and Kuang [18]
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