How might model uncertainty and transaction costs impact retained earning & dividend strategies? An examination through a classical insurance risk model

Model uncertainty and ambiguity aversion have important consequences for decision-making under uncertainty in diverse fields such as insurance, finance and economics. Although model uncertainty has been considered in decision-making problems in finance and economics, as well as problems relevant to (re)-insurance, relatively little attention has been given to exploring implications of model uncertainty and ambiguity aversion for the optimal policies governing cash retention and dividend payout. On the other hand, taxes and transaction costs/fees have a significant impact on retained earnings and dividend strategies. Despite its technically challenging, their impacts on optimal dividend strategies have been studied in the literature. However, consequences of model uncertainty and ambiguity aversion for optimal dividend payout policies and related decision-making issues in the presence of transaction costs/taxes have not been well-understood. This paper aims to explore this relatively unknown zone and to articulate this technically challenging problem. Specifically, we shall provide a rigorous approach to examine the impacts of model uncertainty and ambiguity aversion on optimal cash retention and dividend payout strategies with fixed and proportional transaction costs/taxes. Our key findings include (1) model uncertainty and ambiguity aversion change the qualitative behaviour of optimal strategies. Say the optimal strategy is a multi-level lump-sum strategy and tends to have more levels than that of the problem without capturing model uncertainty (2) the value function tends to be rougher (in terms of smoothness) than that of the problem without incorporating model uncertainty.