Neofytos Rodosthenous

Beating the Omega Clock:

Optimal Strategies for Nervous and Impatient Investors

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 these investors under such adverse market conditions. In mathematical terms, we study the optimal selling of an asset in a random time-horizon under spectrally negative Lèvy models. The random time-horizon is modelled by an alarm of the so-called Omega default clock in insurance literature, which goes off when the cumulative amount of time spent by the asset price in an undesirable low region exceeds an independent exponential random time. In addition to the traditional profit-taking exercising strategy, we prove mathematically that the real-life employed stop-loss and trailing-stop strategies are also optimal under “high levels” of impatience and severe anxiety of the investors. We give a complete characterisation of all optimal exercising thresholds.

(Joint work with H. Zhang)

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