Advances and Applications in Statistics
Volume 2, Issue 1, Pages 79 - 99
(April 2002)
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DECISION RISK REDUCTIONS FOR STOCK INDICES
Wolfgang Stummer (Germany)
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Abstract: We model
the dynamics Xt of a stock index
as a non-lognormally-distributed generalization of
the geometric Brownian motion. In detail, Xt
is supposed to be a weak solution of a
one-dimensional stochastic differential equation of
the form
dXt
= b(Xt)dt
+ sXtdWt,
with volatility
s > 0 and Brownian motion
Wt. For a dichotomous Bayesian
decision problem concerning the size of the drift
b, we investigate the (average) reduction
of decision risk that can be obtained by observing
the path of X. |
Keywords and phrases: Bayesian decision problem, generalized Black/Scholes context, Ia-divergence. |
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