Asymptotic properties of extrema of compound Cox processes and their applications to some problems of financial mathematics (Q2752973)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Asymptotic properties of extrema of compound Cox processes and their applications to some problems of financial mathematics |
scientific article; zbMATH DE number 1665907
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic properties of extrema of compound Cox processes and their applications to some problems of financial mathematics |
scientific article; zbMATH DE number 1665907 |
Statements
22 October 2001
0 references
sum
0 references
maximum
0 references
Wiener process
0 references
convergence
0 references
independent summands
0 references
Asymptotic properties of extrema of compound Cox processes and their applications to some problems of financial mathematics (English)
0 references
A Cox process is considered. A realization of the process on a given interval determines the number of summands in the sum of i.i.d. random variables, having zero expectations and finite variances. The maximum and minimum of this sum are investigated when the length of this interval increases. Necessary and sufficient conditions for the normalized maxima and minima to converge in probability are proved. The limit distributions of these values are expressed in terms of distribution of a maximum of the standard Wiener process on a given interval. The obtained results are applied to prediction of stock prices in the situation where the intensity of stock trade increases unboundedly.
0 references
