@misc{1944648,
  abstract     = {We consider optimal stopping problems for ambiguity averse decision makers with multiple priors. In general, backward induction fails. If, however, the class of priors is time-consistent, we establish a generalization of the classical theory of optimal stopping. To this end, we develop first steps of a martingale theory for multiple priors. We define minimax (super)martingales, provide a Doob-Meyer decomposition, and characterize minimax martingales. This allows us to extend the standard backward induction procedure to ambiguous, time-consistent preferences. The value function is the smallest process that is a minimax supermartingale and dominates the payoff process. It is optimal to stop when the current payoff is equal to the value function. Moving on, we study the infinite horizon case. We show that the value process satisfies the same backward recursion (Bellman equation) as in the finite horizon case. The finite horizon solutions converge to the infinite horizon solution. Finally, we characterize completely the set of time-consistent multiple priors in the binomial tree. We solve two classes of examples: the so-called independent and indistinguishable case (the parking problem) and the case of American Options (Cox-Ross-Rubinstein model).},
  author       = {Riedel, Frank},
  issn         = {0931-6558},
  language     = {English},
  number       = {390},
  publisher    = {Universit{\"a}t Bielefeld},
  title        = {Optimal Stopping under Ambiguity},
  year         = {2007},
}

TY  - GEN
ID  - 1944648
TI  - Optimal Stopping under Ambiguity
AU  - Riedel, Frank
PY  - 2007
AB  - We consider optimal stopping problems for ambiguity averse decision makers with multiple priors. In general, backward induction fails. If, however, the class of priors is time-consistent, we establish a generalization of the classical theory of optimal stopping. To this end, we develop first steps of a martingale theory for multiple priors. We define minimax (super)martingales, provide a Doob-Meyer decomposition, and characterize minimax martingales. This allows us to extend the standard backward induction procedure to ambiguous, time-consistent preferences. The value function is the smallest process that is a minimax supermartingale and dominates the payoff process. It is optimal to stop when the current payoff is equal to the value function. Moving on, we study the infinite horizon case. We show that the value process satisfies the same backward recursion (Bellman equation) as in the finite horizon case. The finite horizon solutions converge to the infinite horizon solution. Finally, we characterize completely the set of time-consistent multiple priors in the binomial tree. We solve two classes of examples: the so-called independent and indistinguishable case (the parking problem) and the case of American Options (Cox-Ross-Rubinstein model).
KW  - Ambiguity
KW  - Optimal stopping
KW  - Uncertainty aversion
IS  - 390
PB  - Universität Bielefeld
SN  - 0931-6558
U3  - PUB:ID 1944648
UR  - http://www.imw.uni-bielefeld.de/papers/files/imw-wp-390.pdf
UR  - http://nbn-resolving.de/urn:nbn:de:hbz:361-10784
ER  -