JOINT DISTRIBUTIONS OF THE MAXIMUM DRAWDOWN AND MAXIMUM DRAWUP IN LÉVY PROCESSES

Date

2025-7-7

Author

Akdoğan, Emre

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The maximum drawdown and maximum drawup variables in a certain time period have attracted the attention of investors and have been used as dynamic risk measures. This thesis aims to derive the joint probability distributions of the maximum drawdown and maximum drawup amounts under a \lv process framework. For the first time, the joint distributions are studied under the \lv process model. Establishing the relationship between these variables through joint distributions enables the estimation of one variable given the other. The Doob-$h$ transforms of the process from infimum to supremum and post-supremum process have been previously obtained in the literature via path decomposition conditioned on the extreme values of the \lv process. However, characterizing the process up to the infimum and determining the distribution of the maximum drawdown within this region remains an open research question. This thesis addresses this gap by introducing novel methods, revealing how the maximum drawdown and maximum drawup vary with each other.

Subject Keywords

Lévy Process, Maximum Drawdown, Maximum Drawup, Path Decomposition, Doob-h Transform

URI

https://hdl.handle.net/11511/115469

Collections

Graduate School of Applied Mathematics, Thesis