Nonlinear averaging axioms in financial mathematics
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 4, pp. 800-810
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In the presence of an uncertainty factor, that is, if
some variable $X$ assumes several values
$x_1,\ldots, x_n$ rather than a single value, one usually performs
an averaging over these values
with some coefficients (measures) $\alpha_i$ such that $\sum_{i=1}^n\alpha_i=1$ and sets
$y=\sum\alpha_ix_i$. For an equity market, there arises a
nonlinear averaging for $y$. We consider
an averaging of the form $f(y)=\sum\alpha_if_i(x_i)$.
Starting from four natural axioms, we prove
that either the above-mentioned linear averaging holds,
or $y=\log\sum_{i=1}^ne^{x_i}$. An
example of a stock price breakout under this summation is given.
Keywords:
expectation, uncertainty factor, value of a random variable, bank, stock, financial dynamics, stock price breakout.
Mots-clés : profit
Mots-clés : profit
@article{TVP_2003_48_4_a9,
author = {V. P. Maslov},
title = {Nonlinear averaging axioms in financial mathematics},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {800--810},
publisher = {mathdoc},
volume = {48},
number = {4},
year = {2003},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_4_a9/}
}
V. P. Maslov. Nonlinear averaging axioms in financial mathematics. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 4, pp. 800-810. http://geodesic.mathdoc.fr/item/TVP_2003_48_4_a9/