6 INTRODUCTION
applications, such as automated wealth management, hedge fund management, and
quantitative trading. In the following, to better understand the idea, we begin by
introducing a concrete example of real-life OLPS applications.
Suppose Bin, a 30-year-old man, has a capital of $10,000, and he wants to increase
the capital to $1,000,000
∗
when he retires at 60 years old, such that he can maintain
his current living standards.Assume he has no extra income for investment and purely
relies on the initial capital. He would like to achieve this target via the investments
in financial markets. Assume that his investment consists of three assets, including
Microsoft (stock, symbol: “MSFT”), Goldman Sachs (stock, symbol: “GS”), and
Treasury bill.
†
All historical records on the three assets, mainly price quotes, are
publicly available. Then, every month,
‡
Bin receives updated information about the
three assets and has to face a crucial challenge of decision making, that is, “How
to allocate (rebalance) his capital
§
among the three assets every month such that his
capital will be more likely increased in the future?” The idea of exploring OLPS
technology is to help Bin automate the sequences of allocation/rebalancing decisions
so as to maximize his investment return in the long run.
In literature, there are two major schools of principles and theories for portfolio
selection: (i) Markowitz’s mean variance theory (Markowitz 1952, 1959) that trades
off between the expected return (mean) and risk (variance) of a portfolio, which is
suitable for single-period portfolio selection and (ii) capital growth theory (or Kelly
investment) (Kelly 1956; Breiman 1961; Thorp 1971; Finkelstein and Whitley 1981)
that aims to maximize the expected log return of a portfolio and naturally addresses
multiple-period investment. Due to the sequential nature of a real-world portfolio
selection task, many recent OLPS techniques often design algorithms by following
the second family of principles and theories.
Note that this book is focused on the algorithmic aspects, rather than the the-
ory (Breiman 1960; Thorp 1969, 1997; Hakansson 1970, 1971; MacLean et al. 2011).
Our study is often concerned with investment management involving multiple types
of assets, which may include fixed income securities, equities, and derivatives. Our
study is also different from another great body of existing work, which attempted to
forecast financial time series by applying computational intelligence techniques and
conduct single-stock trading (Katz and McCormick 2000; Huang et al. 2011), such as
reinforcement learning (Moody et al. 1998; Moody and Saffell 2001), online predic-
tion (Koolen and Vovk 2012), boosting and expert weighting (Creamer 2007, 2012;
Creamer and Freund 2007, 2010; Creamer and Stolfo 2009), neural networks (Kimoto
et al. 1993; Dempster et al. 2001), decision trees (Tsang et al. 2004), and support
vector machines (Tay and Cao 2001; Cao and Tay 2003; Lu et al. 2009). Finally,
we emphasize the nature of “online” algorithms for addressing the portfolio selec-
tion problem, in which the algorithms must be computationally efficient enough
∗
Here, one million is an arbitrary number; of course, the more the better.
†
Treasury bill is often regarded as a risk-free asset, earning a guaranteed risk-free return. Once he does
not want to buy any stocks, he can put all money in Treasury bills, instead of cash.
‡
Here, “month” represents a period, which can be one day, one week, or one month, etc.
§
For example, he may buy $5000 MSFT stock, $3000 GS stocks, and $2000 Treasury bills.
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