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October 17, 2025

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

Key Points

The study demonstrates optimal strategies for managing dividends under dual risks in a diffusion framework.
Expected total discounted dividends are expressed through integro-differential equations, showing clear outcomes.
Explicit solutions for dividend strategies are derived when profits follow exponential distribution patterns.
Numerical examples support theoretical findings by analyzing parameter effects within the risk model.

Abstract

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.

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

Key Points

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