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Real Options Under Ambiguity With Rare Events

We consider a real-options problem in which the underlying project value follows a geometric or exponential Levy process, capturing rare events besides continuous fluctuations. Such rare events lead to ambiguity because of inconclusive empirical data or market incompleteness. We use ambiguity theory leveraging the notion of variational preferences and $g$-expectations to pin down for the general case a pricing kernel under which to value real options and derive the firm's optimal real-option exercise strategy under this pricing kernel. We also provide sufficient conditions for the optimality of a threshold policy in the general case. For the specialized case with multi-priors preferences, we} obtain explicit expressions for the optimal investment threshold, expected investment time, and value function {\color{blue} and prove comparative statics to assess analytically the effect of small jumps on these. Closed-form expressions are not readily available for multipliers preferences, but we provide approximate solutions for the cases with negligible and deep ambiguity.} Rare events, which are priced under ambiguity aversion, generally lead to a higher investment threshold, delayed investment and higher option value.