Learning optimal stopping rules and stopping environments

• Applicants: Professor Dr. Stefan Ankirchner; Professor Dr. Sören Christensen
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 547236699

The aim of the project is to develop methods for analyzing learning strategies for stopping problems. A stopping problem arises whenever an economic agent wants to stop a stochastic process in such a way that the process value is maximized in expectation at the stopping time. The starting point of the project are situations in which, firstly, the agent has to solve the same stopping problem in many successive rounds, whereby the processes to be stopped are independent but identically distributed; and secondly, the agent does not know the distribution of the processes to be stopped at the beginning. By observing the individual stopped process realizations, the agent can learn the process distribution and consequently approximate the optimal stopping rule better and better. In the project we will investigate strategies for learning optimal stopping rules and compare them with the help of the so-called regret. A regret arises if the agent chooses a suboptimal stopping rule due to an estimation error. Formally, the regret in a round is defined as the difference between the expected payoff under the optimal stopping time and the expected payoff under the actually chosen stopping time. One project focus is the asymptotic rate at which the regret converges to zero as the number of rounds increases. A specific goal is to determine sharp lower bounds for the rate that no strategy can fall below. Another goal is to develop explicit strategies that attain the lower bound and are optimal in this sense. These goals are also set for the extended problem, where in each round the agent must first select a stopping environment and then a stopping time within this environment.

• DFG Programme: Research Grants