Tools to estimate the first passage time to a convex barrier
2005 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 42, no 1, 61-81 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2005. Vol. 42, no 1, 61-81 p.
IdentifiersURN: urn:nbn:se:su:diva-24364OAI: oai:DiVA.org:su-24364DiVA: diva2:197379
Part of urn:nbn:se:su:diva-6972005-10-202005-10-202010-09-13Bibliographically approved