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Confidence regions of minimal area for the scale-location parameter and their applications

A. Czarnowska;  A. V. Nagaev — 2001

Applicationes Mathematicae

The area of a confidence region is suggested as a quality exponent of parameter estimation. It is shown that under very mild restrictions imposed on the underlying scale-location family there exists an optimal confidence region. Explicit formulae as well as numerical results concerning the normal, exponential and uniform families are presented. The question how to estimate the quantile function is also discussed.

Asymptotics of riskless profit under selling of discrete time call options

A. V. Nagaev;  S. A. Nagaev — 2003

Applicationes Mathematicae

A discrete time model of financial market is considered. In the focus of attention is the guaranteed profit of the investor which arises when the jumps of the stock price are bounded. The limit distribution of the profit as the model becomes closer to the classic model of geometrical Brownian motion is established. It is of interest that the approximating continuous time model does not assume any such profit.

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