Optimal bailout ratcheting of dividends under a Brownian risk model
Abstract
This paper investigates the optimal control problem of ratcheting dividend with capital injection under a Brownian risk model. We show that the value function is the unique viscosity solution to the associated Hamilton–Jacobi–Bellman equation. Explicit analytical expressions of the value function and the optimal strategy are obtained when the general ratcheting dividend strategies are restricted as finite ratcheting dividend strategies (i.e. the dividend rate takes only a finite number of values), where the optimal dividend strategy is the threshold-type finite ratcheting dividend strategy, and the optimal capital injection strategy is the bailout strategy. Some numerical illustrations are provided at the end.
Fields of Study & Subjects
Probability and Risk Models
Stochastic processes and financial applications
Risk and Portfolio Optimization
Publication details
- Journal / source
- Scandinavian Actuarial Journal
- Volume
- 2026
- Issue
- 8
- Pages
- 825–850
- Publication date
- 28 January 2026
- Language
- EN