A Two‐Dimensional Diffusion Dual Risk Model With Random Delays Under the Threshold Strategy

ABSTRACT This paper investigates the dividend problem for a two‐dimensional diffusion dual risk model with random delays in profit arrival times. We prove the optimality of threshold dividend strategies. Under this strategy, we derive a set of integro‐differential equations for the expected total discounted dividends until ruin. Explicit solutions are obtained when profits follow an exponential distribution, while the Laplace transform method is applied for general profit distributions. Numerical examples validate the theoretical results and analyze parameter effects on the risk model.