Optimal Betting Strategy

This lecture discusses the formulation of a gambling problem as a dynamic programming task, focusing on maximizing the expected logarithm of terminal capital. It covers planning horizon, state space, action space, and terminal cost. The lecture explains the dynamic programming solution process, including initialization and backward induction. It presents the optimal betting policy for each round and the expected terminal wealth under this policy. The lecture also explores the impact of different utility functions on the optimal betting strategy, highlighting the importance of risk preference in decision-making.