We study the optimal liquidation strategy for a call spread in the case when the market uses an over-estimated volatility to price options. The problem is formulated as an optimal stopping problem, which we solve explicitly.

We consider the problem of quickest detection of abrupt changes for processes that are not necessarily independent and identically distributed (i.i.d.) before and after the change. By making a very simple observation that applies to most well-known optimum stopping times developed for this problem (in particular CUSUM and Shiryayev–Roberts stopping rule) we show that their optimality can be eas...

One of the more well-known unsolved problems in number theory is the Collatz (3n + 1) Conjecture. The conjecture states that iterating the map that takes even n ∈ N to n 2 and odd n to 3n+1 2 will eventually yield 1. This paper is an exploration of this conjecture on positive integers of the form 2kb − m and 3kb − 1, and stems from the work of the first author’s Senior Seminar research. We take...

Objectives It is well known that a sequentially monitored clinical trial that stops early for benefit has a crude treatment difference that overestimates the true treatment effect. This has led to extended debate in the literature, with some researchers arguing that early stopping is an important source of bias in meta-analyses of clinical trials. We therefore investigated the implications of e...