Ill-posed problems in technical
analysis and market stability.
Author: Alexander Ilyinsky
All traders in stock and FX markets may be referred as chartists and fundamentalists.
The importance of such division of traders into these groups and the destabilazing role of
chartists have been first demonstrated by Frankel and Froot (1988).
The chartists or noise traders make a choice of their strategy to buy or sell using
only market price-volume data. The fundamentalists or sophisticated traders try to
evaluate "fundamental" or true value of assets analyzing sales, earning as well
as the management of the company and government policy. Due to mobility there is a
exchange of traders between these two group.
The chartists may be divided in turn optimistic bulls and pessimistic bears. The
relative populations of bears and bulls depend on market price trend identification by
chartist traders.
The destabilyzing positive feedback between flow of buy/sell orders and
positive/negative price trend exists and collective actions of chartists could lead to
market bubble formation. During positive (or bulls) trend the bulls population grows at
expense of bears and fundamentalists. During negative (or bears) trend the bulls
population decreases.
The strategy selected by chartist depends on numerical evaluation of price trend dp/dt.
The numerical differentiation of empirical data is the ill-posed problem and causes a
tremendous noise amplification.
In present paper a different regularization procedures for trend identification are
compared and different procedures for selection of regularization parameters are
discussed. The stabilyzing effect of ill-posedness of trend evaluation has been shown.
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