Part II
Principles
17
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PRINCIPLES 19
Existing online portfolio selection (OLPS) approaches follow the preceding problem
formulations and derive explicit portfolio update schemes. Table II.1 (Li and Hoi
2014) summarizes the main principles and several representative algorithms, and
four of the algorithms are illustrated in detail in later chapters. In particular, first
we introduce several benchmark algorithms. Then, we introduce three categories of
principles or algorithms with explicit portfolio update schemes, which are classified
according to the directions of weight transfer. The first approach, follow the winner,
increases the weights of more successful experts or stocks, often based on their his-
torical performance. Contrarily, the second approach, follow the loser, increases the
weights of less successful experts or stocks, or transfers the weights from winners
to losers. The third category, the pattern matching–based approach, constructs port-
folios based on similar historical patterns and has no explicit directions. Finally, we
survey some related meta-algorithms applying to a set of experts, each of which is
equipped with any algorithms in the preceding three categories.
This part is organized as follows. Chapter 3 surveys the benchmarks used in this
study. Chapter 4 surveys the first principle, follow the winner. Chapter 5 surveys the
second principle, follow the loser. Then, Chapter 6 introduces the third principle, pat-
tern matching–based approaches. The final principle, meta-algorithms, is introduced
in Chapter 7.
Table II.1 Principles and representative online portfolio selection algorithms
Classifications Algorithms Representative References
Benchmarks Buy and Hold
Best Stock
Constant Rebalanced Portfolios Kelly (1956); Cover (1991)
Follow
the winner
Universal Portfolios Cover (1991)
Exponential Gradient Helmbold et al. (1998)
Follow the Leader Gaivoronski and Stella (2000)
Follow the Regularized Leader Agarwal et al. (2006)
Aggregating-Type Algorithms Vovk and Watkins (1998)
Follow
the loser
Anticorrelation Borodin et al. (2004)
Passive–Aggressive Mean
Reversion
Li et al. (2012)
Confidence Weighted Mean
Reversion
Li et al. (2013)
Online Moving Average
Reversion
Li et al. (2015)
Robust Median Reversion Huang et al. (2013)
(Continued)
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20 PRINCIPLES
Table II.1 (Continued) Principles and representative online portfolio selection algorithms
Classifications Algorithms Representative References
Pattern
matching–
based
approaches
Nonparametric Histogram
Log-Optimal Strategy
Györfi et al. (2006)
Nonparametric Kernel-Based
Log-Optimal Strategy
Györfi et al. (2006)
Nonparametric Nearest
Neighbor Log-Optimal
Strategy
Györfi et al. (2008)
Correlation-Driven
Nonparametric Learning
Strategy
Li et al. (2011a)
Nonparametric Kernel-Based
Semi-Log-Optimal Strategy
Györfi et al. (2007)
Nonparametric Kernel-Based
Markowitz-Type Strategy
Ottucsák and Vajda (2007)
Nonparametric Kernel-Based
GV-Type Strategy
Györfi and Vajda (2008)
Meta-
algorithms
Aggregating Algorithm Vovk (1990); Vovk and
Watkins (1998)
Fast Universalization Algorithm Akcoglu et al. (2005)
Online Gradient Updates Das and Banerjee (2011)
Online Newton Updates Das and Banerjee (2011)
Follow the Leading History Hazan and Seshadhri (2009)
Source: Li and Hoi (2014).
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