Optimal stopping under ambiguity in continuous time - Frank Riedel (Bielefeld University, Institute of Mathematical Economics (IMW), 2010)
We develop a theory of optimal stopping problems under ambiguity in continuous time. Using results from (backward) stochastic calculus, we characterize the value function as the smallest (nonlinear) supermartingale dominating the payoff process. For Markovian models, we derive an adjusted Hamilton-Jacobi-Bellman equation involving a nonlinear drift term that stems from the agent's ambiguity aversion. We show how to use these general results for search problems and American Options.
urn:nbn:de:hbz:361-16765
Keywords: D81; C61; G11; 330; Optimal stopping; Ambiguity; Uncertainty aversion; Robustness; Continuous time; Optimal control; Entscheidung bei Unsicherheit; Suchtheorie; Risikoaversion; Theorie