By Jin-Yi Cai
This number of contemporary papers on computational complexity idea grew out of actions in the course of a unique yr at DIMACS. With contributions via a number of the top specialists within the box, this publication is of lasting worth during this fast-moving box, delivering expositions now not chanced on somewhere else. even if aimed essentially at researchers in complexity concept and graduate scholars in arithmetic or laptop technological know-how, the publication is on the market to someone with an undergraduate schooling in arithmetic or desktop technology. by means of referring to a few of the significant subject matters in complexity idea, this publication sheds gentle in this burgeoning zone of study.
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M, represents the proportion of wealth invested in asset i at the beginning of the t-th period. Typically, the portfolio is ∗ When m = 1, the problem is reduced to single-stock trading, which is out of the scope of this book. †A period can be a week, a day, an hour, or even a second in high-frequency trading. , pt,i −pt−1,i . pt−1,i For the calculation of the first period, suppose we have p0,i . § For example, x = 2 means that the investment on an asset will increase by 100%, or double its t,i initial investment.
1998; Agarwal et al. 2006), we relax this constraint and evaluate it empirically. 000238). With such a setting, a new asset named “margin component” is generated for each asset, and its price relative for period t equals 2 × xt,i − 1 − c. In the case of xt,i ≤ 1+c 2 , which means the stock drops more than half, we simple set its margin component to 0 (Li et al. † As a result, if margin buying is allowed, the total number of assets becomes 2m. 3 Evaluation One standard criterion to evaluate an OLPS strategy is its portfolio cumulative wealth at the end of trading periods.
2005) extended Cover’s UP from a parameterized CRP class to a wide class of investment strategies, including trading strategies operating on a single stock and portfolio strategies operating on the whole stock market. Kozat and Singer (2011) proposed a similar universal algorithm based on the class of semiconstant rebalanced T&F Cat #K23731 — K23731_C004 — page 24 — 9/28/2015 — 21:07 EXPONENTIAL GRADIENT 25 portfolios (Helmbold et al. 1998), which provides good asymptotic performance in case of nonzero transaction costs.