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Tools to estimate t...
Tools to estimate the first passage time to a convex barrier
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- Hammarlid, Ola (författare)
- Stockholms universitet,Matematiska institutionen
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(creator_code:org_t)
- 2005
- 2005
- Engelska.
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Ingår i: Journal of Applied Probability. - 0021-9002 .- 1475-6072. ; 42:1, s. 61-81
- Relaterad länk:
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https://urn.kb.se/re...
Abstract
Ämnesord
Stäng
- he first passage time of a random walk to a barrier (constant or concave) is of great importance in many areas, such as insurance, finance, and sequential analysis. Here, we consider a sum of independent, identically distributed random variables and the convex barrier cb(n/c), where c is a scale parameter and n is time. It is shown, using large-deviation techniques, that the limit distribution of the first passage time decays exponentially in c. Under a tilt of measure, which changes the drift, four properties are proved: the limit distribution of the overshoot is distributed as an overshoot over a linear barrier; the stopping time is asymptotically normally distributed when it is properly normalized; the overshoot and the asymptotic normal part are asymptotically independent; and the overshoot over a linear bather is bounded by an exponentially distributed random variable. The determination of the function that multiplies the exponential part is guided by consideration of these properties.
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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