A delayed dual risk model

Paper: arXiv 2301.06450

Authors: Lingjiong Zhu

Abstract

In this paper, we study a dual risk model with delays in the spirit of Dassios-Zhao. When a new innovation occurs, there is a delay before the innovation turns into a profit. We obtain large initial surplus asymptotics for the ruin probability and ruin time distributions. For some special cases, we get closed-form formulas. Numerical illustrations will also be provided.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents rigorous mathematical analysis of a delayed dual risk model, deriving asymptotics for ruin probabilities and closed-form solutions for special cases. However, it lacks extensive empirical validation or real-world financial dataset testing, relying primarily on theoretical derivations and basic numerical illustrations.

Research Flowchart

  flowchart TD
    A["Research Goal: Analyze ruin probability & time<br>in dual risk model with innovation delays"] --> B["Input Model: Surplus process with delayed profits<br>(Dassios-Zhao framework)"]
    B --> C["Apply Asymptotic Analysis & Renewal Theory"]
    C --> D["Derive Asymptotics for Large Initial Surplus"]
    C --> E["Solve Closed-Form Formulas for Special Cases"]
    D --> F["Perform Numerical Simulations"]
    E --> F
    F --> G["Outcomes: Precise ruin probabilities &<br>time distributions for delayed profits"]