November 7, 2019, 11:00–12:15
We consider decision makers who are impatient when the prices of their assets are in undesirable low regions for a significant amount of time, and they are also nervous and risk averse to negative price jumps. We wish to study the unusual reactions of investors under such adverse market conditions. In mathematical terms, we study the optimal selling of an asset under Lévy models with negative jumps. The random time-horizon / discount rate is modelled via the so-called Omega default clock in insurance literature, which counts the cumulative amount of time spent by the asset price in an undesirable low region. This is an attempt to bridge behavioural finance aspects with financial mathematics. In addition to the traditional profit-taking selling strategy, we prove mathematically that the real-life employed stop-loss strategies and trailing stops are also optimal under “high levels” of impatience and nervousness of the investors. We give a complete characterization of all optimal selling thresholds.