10,391 research outputs found
Multilinear Superhedging of Lookback Options
In a pathbreaking paper, Cover and Ordentlich (1998) solved a max-min
portfolio game between a trader (who picks an entire trading algorithm,
) and "nature," who picks the matrix of gross-returns of all
stocks in all periods. Their (zero-sum) game has the payoff kernel
, where is the trader's final wealth and
is the final wealth that would have accrued to a deposit into the best
constant-rebalanced portfolio (or fixed-fraction betting scheme) determined in
hindsight. The resulting "universal portfolio" compounds its money at the same
asymptotic rate as the best rebalancing rule in hindsight, thereby beating the
market asymptotically under extremely general conditions. Smitten with this
(1998) result, the present paper solves the most general tractable version of
Cover and Ordentlich's (1998) max-min game. This obtains for performance
benchmarks (read: derivatives) that are separately convex and homogeneous in
each period's gross-return vector. For completely arbitrary (even
non-measurable) performance benchmarks, we show how the axiom of choice can be
used to "find" an exact maximin strategy for the trader.Comment: 41 pages, 3 figure
On-Line Portfolio Selection with Moving Average Reversion
On-line portfolio selection has attracted increasing interests in machine
learning and AI communities recently. Empirical evidences show that stock's
high and low prices are temporary and stock price relatives are likely to
follow the mean reversion phenomenon. While the existing mean reversion
strategies are shown to achieve good empirical performance on many real
datasets, they often make the single-period mean reversion assumption, which is
not always satisfied in some real datasets, leading to poor performance when
the assumption does not hold. To overcome the limitation, this article proposes
a multiple-period mean reversion, or so-called Moving Average Reversion (MAR),
and a new on-line portfolio selection strategy named "On-Line Moving Average
Reversion" (OLMAR), which exploits MAR by applying powerful online learning
techniques. From our empirical results, we found that OLMAR can overcome the
drawback of existing mean reversion algorithms and achieve significantly better
results, especially on the datasets where the existing mean reversion
algorithms failed. In addition to superior trading performance, OLMAR also runs
extremely fast, further supporting its practical applicability to a wide range
of applications.Comment: ICML201
Universal Codes from Switching Strategies
We discuss algorithms for combining sequential prediction strategies, a task
which can be viewed as a natural generalisation of the concept of universal
coding. We describe a graphical language based on Hidden Markov Models for
defining prediction strategies, and we provide both existing and new models as
examples. The models include efficient, parameterless models for switching
between the input strategies over time, including a model for the case where
switches tend to occur in clusters, and finally a new model for the scenario
where the prediction strategies have a known relationship, and where jumps are
typically between strongly related ones. This last model is relevant for coding
time series data where parameter drift is expected. As theoretical ontributions
we introduce an interpolation construction that is useful in the development
and analysis of new algorithms, and we establish a new sophisticated lemma for
analysing the individual sequence regret of parameterised models
Hypotheses testing on infinite random graphs
Drawing on some recent results that provide the formalism necessary to
definite stationarity for infinite random graphs, this paper initiates the
study of statistical and learning questions pertaining to these objects.
Specifically, a criterion for the existence of a consistent test for complex
hypotheses is presented, generalizing the corresponding results on time series.
As an application, it is shown how one can test that a tree has the Markov
property, or, more generally, to estimate its memory
Can We Learn to Beat the Best Stock
A novel algorithm for actively trading stocks is presented. While traditional
expert advice and "universal" algorithms (as well as standard technical trading
heuristics) attempt to predict winners or trends, our approach relies on
predictable statistical relations between all pairs of stocks in the market.
Our empirical results on historical markets provide strong evidence that this
type of technical trading can "beat the market" and moreover, can beat the best
stock in the market. In doing so we utilize a new idea for smoothing critical
parameters in the context of expert learning
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