Balancing Suspense and Surprise: Timely Decision Making with Endogenous
  Information Acquisition
  We develop a Bayesian model for decision-making under time pressure with
endogenous information acquisition. In our model, the decision maker decides
when to observe (costly) information by sampling an underlying continuous-time
stochastic process (time series) that conveys information about the potential
occurrence or non-occurrence of an adverse event which will terminate the
decision-making process. In her attempt to predict the occurrence of the
adverse event, the decision-maker follows a policy that determines when to
acquire information from the time series (continuation), and when to stop
acquiring information and make a final prediction (stopping). We show that the
optimal policy has a rendezvous structure, i.e. a structure in which whenever a
new information sample is gathered from the time series, the optimal "date" for
acquiring the next sample becomes computable. The optimal interval between two
information samples balances a trade-off between the decision maker's surprise,
i.e. the drift in her posterior belief after observing new information, and
suspense, i.e. the probability that the adverse event occurs in the time
interval between two information samples. Moreover, we characterize the
continuation and stopping regions in the decision-maker's state-space, and show
that they depend not only on the decision-maker's beliefs, but also on the
context, i.e. the current realization of the time series.
