In this chapter we survey recent research on models of consumption and investment in the presence of stopping choices, such as choices of retirement times. The problems in these models are mixtures of problems regarding consumption/investment and those regarding choices of stopping times. We describe the models, emphasizing their common features, and explain two solution techniques: the dynamic programming approach and the martingale/duality approach. We also explain a common economic intuition derivable from the solutions to the models. Namely, the possibility of stopping is similar to a real option and induces investors to consume less and take more risk than they would in the absence of such possibility.
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