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This paper explores the biases that can arise when individuals have the opportunity to seek information that would allow them to avoid a potentially catastrophic financial event. We focus on a stylized case where an investor makes a series of choices whether to put funds into a safe asset that yields a certain small return or a risky asset that yields a much higher return but that also carries the risk of a catastrophic loss. At each point in time, the investor can gather information at a cost that provides information about the probability that the catastrophic loss would occur in a given period. We first explore this problem theoretically, showing that if investors hold reference-dependent preferences they will not only be more inertial in choosing the risky asset, but also value information asymmetrically, with those holding positions in the risky asset undervaluing information (an ostrich effect) while those holding positions in the safe asset overvaluing information (a curiosity effect), relative to risk-neutral optimal benchmarks. We then report the findings of an experimental investigation in which participants display this state dependence when deciding whether to purchase information, as well a number of other biases in both information gathering and asset choice. Among the findings is that information-gathering is influenced by hedonic factors that would not arise in a normative assessment of information value, such as how close participants are to achieving a wealth goal and curiosity among those no longer subject to risk.