Maximum Drawdown and Drawdown Duration of Spectrally Negative Levy Processes Decomposed at Extremes

Vardar Acar C., Caglar M., Avram F.

JOURNAL OF THEORETICAL PROBABILITY, vol.34, no.3, pp.1486-1505, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.1007/s10959-020-01014-z
  • Journal Name: JOURNAL OF THEORETICAL PROBABILITY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.1486-1505
  • Keywords: Drawdown duration, Maximum drawdown, Scale function, Extreme values, Doob h-transform, PATH DECOMPOSITIONS, INFIMUM
  • Middle East Technical University Affiliated: No

Abstract

Path decomposition is performed to characterize the law of the pre-/post-supremum, post-infimum and the intermediate processes of a spectrally negative Levy process taken up to an independent exponential time T. As a result, mainly the distributions of the supremum of the post-infimum process and the maximum drawdown of the pre-/post-supremum, post-infimum processes and the intermediate processes are obtained together with the law of drawdown durations.