Seminar on Distribution of Maximum Loss for Fractional Brownian Motion

Mine Çağlar

Speaker: Mine Çağlar

Koç University, Department of Mathematics

mcaglar@ku.edu.tr

Seminar: Distribution of Maximum Loss for Fractional Brownian Motion

Date / Time: 19.2.2012 / 15.30

Place: IAM – S209 (Seminar Room)

Abstract

The maximum loss is one way of measuring the risk of falling prices. The price of a volatile asset can be modeled using fractional Brownian motion with Hurst parameter H > 1/2. The advantage of modeling with fractional Brownian motion over Markov processes is its capability of exposing the long range dependence in log-returns. We find bounds on the distribution of the maximum loss for fractional Brownian motion with H > 1/2 and derive estimates on its tail probability. Asymptotically, the tail of the distribution of maximum loss over [0, t] behaves like the tail of the marginal distribution at time t.
Joint work with Ceren Vardar, TOBB ETU.

Institute of Applied Mathematics, http://www3.iam.metu.edu.tr
Society for Industrial and Applied Mathematics, http://siam.org

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