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We develop a Bayesian model for decision-making under time pressure withendogenous information acquisition. In our model, the decision maker decideswhen to observe (costly) information by sampling an underlying continuous-timestochastic process (time series) that conveys information about the potentialoccurrence or non-occurrence of an adverse event which will terminate thedecision-making process. In her attempt to predict the occurrence of theadverse event, the decision-maker follows a policy that determines when toacquire information from the time series (continuation), and when to stopacquiring information and make a final prediction (stopping). We show that theoptimal policy has a rendezvous structure, i.e. a structure in which whenever anew information sample is gathered from the time series, the optimal "date" foracquiring the next sample becomes computable. The optimal interval between twoinformation samples balances a trade-off between the decision maker's surprise,i.e. the drift in her posterior belief after observing new information, andsuspense, i.e. the probability that the adverse event occurs in the timeinterval between two information samples. Moreover, we characterize thecontinuation and stopping regions in the decision-maker's state-space, and showthat they depend not only on the decision-maker's beliefs, but also on thecontext, i.e. the current realization of the time series.

Balancing Suspense and Surprise: Timely Decision Making with Endogenous Information Acquisition