**Eberhard Mayerhofer**

Department of Mathematics and Statistics, University of Limerick, Limerick V94TP9X, Ireland<EMAIL_ADDRESS>
Received: 27 September 2019; Accepted: 16 October 2019; Published: 18 October 2019

**Abstract:** First, we give a closed-form formula for first passage time of a reflected Brownian motion with drift. This corrects a formula by Perry et al. (2004). Second, we show that the maximum before a fixed drawdown is exponentially distributed for any drawdown, if and only if the diffusion characteristic *μ*/*σ*2 is constant. This complements the sufficient condition formulated by Lehoczky (1977). Third, we give an alternative proof for the fact that the maximum before a fixed drawdown is exponentially distributed for any spectrally negative Lévy process, a result due to Mijatovi´c and Pistorius (2012). Our proof is similar, but simpler than Lehoczky (1977) or Landriault et al. (2017).

**Keywords:** reflected Brownian motion; linear diffusions; spectrally negative Lévy processes; drawdown

**MSC (2010):** 60J65; 60J75


2.3.5. Sensitivity Analysis

Sensitivity analysis was conducted targeting the participants who answered to have been diagnosed as SARS-CoV-2 in the survey in May 2021 only.

#### 2.3.6. Ethical Considerations

All individuals who participated in this study consented to their participation. This study was conducted with the approval of the ethics committee of Hiramatsu Memorial Hospital affiliated with Specified Jisoukai Medical Corporation (ID of approval: 20200925).