Paper: arXiv 2408.00003

Authors: Dhiti Osatakul, Shuanming Li, Xueyuan Wu

Abstract

Our paper explores a discrete-time risk model with time-varying premiums, investigating two types of correlated claims: main claims and by-claims. Settlement of the by-claims can be delayed for one time period, representing real-world insurance practices. We examine two premium principles based on reported and settled claims, using recursively computable finite-time ruin probabilities to evaluate the performance of time-varying premiums. Our findings suggest that, under specific assumptions, a higher probability of by-claim settlement delays leads to lower ruin probabilities. Moreover, a stronger correlation between main claims and their associated by-claims results in higher ruin probabilities. Lastly, the premium adjustment principles based on settled claims experience contribute to higher ruin probabilities compared to those based on reported claims experience, assuming all other factors remain constant. Notably, this difference becomes more pronounced when there is a high likelihood of by-claim delays.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical exploration of discrete-time risk models incorporating bonus-malus systems and delayed claim settlements using recursive formulas. While mathematically complex and well-structured theoretically, it relies entirely on synthetic numerical examples rather than real-world empirical data validation.

Research Flowchart

  flowchart TD
    A["Research Goal: Analyze impact of claim delays & time-varying premiums on ruin probabilities"] --> B["Input Data & Assumptions: Main claims, delayed by-claims, premium principles (Reported vs. Settled)"]
    B --> C["Model Formulation: Discrete-time risk model with time-varying premiums and correlated claims"]
    C --> D["Computational Analysis: Recursive calculation of finite-time ruin probabilities"]
    D --> E["Findings: Higher by-claim delay probability reduces ruin probability"]
    D --> F["Findings: Stronger claim correlation increases ruin probability"]
    D --> G["Findings: Settled-claim premium adjustments yield higher ruin probability than reported-claim adjustments"]

Cited References (34)

  1. Discrete-Time Risk Models with Claim Correlated Premiums in a Markovian Environment (2021) — link
  2. Ruin Probabilities And Capital Requirement for Open Automobile Portfolios With a Bonus‐Malus System Based on Claim Counts (2020) — link
  3. Asymptotics for a delay-claim risk model with diffusion, dependence structures and constant force of interest (2019) — link
  4. On asymptotic finite-time ruin probability of a renewal risk model with subexponential main claims and delayed claims (2019) — link
  5. A Risk Process with Delayed Claims and Constant Dividend Barrier (2019) — link
  6. On a discrete interaction risk model with delayed claims and stochastic incomes under random discount rates (2018) — link
  7. An IBNR–RBNS insurance risk model with marked Poisson arrivals (2018) — link
  8. On the Compound Binomial Risk Model with Delayed Claims and Randomized Dividends (2018) — link
and 26 more
  1. Dividend barrier and ruin problems for a risk model with delayed claims (2017) — link
  2. MEASURING THE IMPACT OF A BONUS-MALUS SYSTEM IN FINITE AND CONTINUOUS TIME RUIN PROBABILITIES FOR LARGE PORTFOLIOS IN MOTOR INSURANCE (2017) — link
  3. Solving an Integral Equation Arising from the Ruin Probability of Long-term Bonus-Malus Systems (2017) — link
  4. Ruin Probabilities with Dependence on the Number of Claims within a Fixed Time Window (2016) — link
  5. Risk models with premiums adjusted to claims number (2015) — link
  6. On a discrete interaction risk model with delayed claims and randomized dividends (2015) — link
  7. On a discrete risk model with delayed claims and a randomized dividend strategy (2015) — link
  8. On a discrete-time risk model with claim correlated premiums (2015) — link
  9. On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes (2014) — link
  10. EXPECTED PRESENT VALUE OF TOTAL DIVIDENDS IN THE COMPOUND BINOMIAL MODEL WITH DELAYED CLAIMS AND RANDOM INCOME (2013) — link
  11. On a discrete-time risk model with delayed claims and dividends (2013) — link
  12. Ruin problems under IBNR dynamics (2011) — link
  13. On the Ruin Problem in an Erlang(2) Risk Model with Delayed Claims (2010) — link
  14. Numerical Evaluation of Continuous Time Ruin Probabilities for a Portfolio with Credibility Updated Premiums (2010) — link
  15. The compound binomial risk model with time-correlated claims (2007) — link
  16. On ultimate ruin in a delayed-claims risk model (2005) — link
  17. A Note on Ruin in a Two State Markov Model1 (2001) — link
  18. Ruin probabilities for time-correlated claims in the compound binomial model (2001) — link
  19. Distributions stationnaires d’un système bonus–malus et probabilité de ruine (1988) — link
  20. Ruin probabilities allowing for delay in claims settlement (1985) — link
  21. “On a discrete time risk model with time-delayed claims and a constant dividend barrier” (2019)
  22. A risk model with varying premiums: Its risk management implications (2015) — link
  23. Ultimate ruin probability in discrete time with Bühlmann credibility premium adjustments (2013)
  24. On an interaction risk model with delayed claims (2004)
  25. If the number of settled claims in the current period is 1, then the premium level for the next period will remain in the current premium level
  26. If the settled aggregate claims in the current period is no more than 3

0 of 34 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.