A Note on Universal Bilinear Portfolios

A note on bilinear forms

Universal Portfolios

We exhibit an algorithm for portfolio selection that asymptotically outperforms the best stock in the market. Let x i = x i 1 ; x i 2 ; : : : ; 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 i 1 ; b i 2 ; : : : ; b im t ; b ij 0; P j b ij = 1 ; denote the proportion b ij of wealth invested in the j-t...

A Note on Self-bilinear Maps

Cryptographic protocols depend on the hardness of some computational problems for their security. Joux briefly summarized known relations between assumptions related bilinear map in a sense that if one problem can be solved easily, then another problem can be solved within a polynomial time [6]. In this paper, we investigate additional relations between them. Firstly, we show that the computati...

A Note on the Three-portfolios Matching Problem

A typical problem arising in the financial planning for private investors consists in the fact that the initial investor’s portfolio, the one determined by the consulting process of the financial institution and the universe of instruments made available to the investor have to be matched/optimized when determining the relevant portfolio choice. We call this problem the three-portfolios matchin...

A Note on the Maximum of a Certain Bilinear Form

In this note a generalization of a result by Hardy, Littlewood and PP olya (1926) is derived on computing the maximum of a certain bilinear form. The proof is elementary.