Paper: arXiv 2410.11846

Authors: Daniel Tawiah Pabifio

Abstract

An insurance company, as a risk bearer, is exposed to the likelihood of running into ruin. This is the situation where the initial surplus falls below zero. There is the need to find the required start-up capital to hedge against insolvency. Most researchers, irrespective of whether the test for claim dependency holds or not, assume claim independence in their computing of ruin probabilities to start up their initial capital. The objective of this study is to carry out comparative sensitivity analysis of ruin probability under both assumptions of dependence and independence, irrespective of whether the data exhibits independence or not, based on data from an insurance company in Ghana. Secondary data from an insurance company was obtained from the National Insurance Commission (NIC) for the period of 2013 to 2017. The study employed copulas to determine the claim dependence among the various insurance products and the company in general. The study concluded that when there is dependence in the claim data, computing the ruin probability based on the assumption of independence results in underestimation. Among the various insurance products, the most profitable insurance product was motor insurance, and Fire and Allied insurance exhibited the highest dependency. At a higher start-up capital, when claims are dependent, assuming independence in calculating the ruin probability results in a significant difference. Hence, it was recommended that insurance companies should adopt the assumption of dependence between the claims data as the initial reserves become larger, particularly for larger insurance companies, to avoid misleading results. Also, awareness of the perils and consequences of fire outbreaks and disasters should be raised to the general public to reduce the risk of frequent occurrence.

Complexity vs Empirical Score

  • Math Complexity: 5.5/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper applies standard copula models and classical ruin theory to an empirical dataset from Ghana’s insurance sector. While it addresses an important practical question regarding claim dependence, the methodological innovation is modest and reproducibility is limited by data availability.

Research Flowchart

  flowchart TD
    A[Goal: Compare Ruin Probability under Claim Dependence vs. Independence] --> B[Data Input: NIC Ghana Insurance Claims Data 2013-2017]
    B --> C[Methodology: Copulas for Claim Dependency & Sensitivity Analysis]
    C --> D[Compute Ruin Probabilities & Reserve Thresholds]
    D --> E[Finding 1: Independence Assumption Underestimates Ruin Probability]
    D --> F[Finding 2: Motor Most Profitable; Fire Exhibits Highest Dependency]
    E --> G[Outcome: Recommend Dependence Models for Large Reserves & Public Fire Awareness]
    F --> G

Cited References (25)

  1. Actuarial mathematics (1997)
  2. The future of the Affordable Care Act and insurance coverage (2017)
  3. Interplay of insurance and financial risks in a stochastic environment (2019)
  4. Ruin with insurance and financial risks following the least risky FGM dependence structure (2015)
  5. Ruin probability-based initial capital of the discrete-time surplus process (2013)
  6. Capital structure of non-life insurance firms In Japan (2016)
  7. The exponential estimate of the ultimate ruin probability for the non-homogeneous renewal risk model (2018)
  8. Catastrophe insurance (2015)
and 17 more
  1. Insurance risk and ruin (2016)
  2. Dividend problems in the dual risk model (2013)
  3. Stochastic claims reserving methods in insurance (2008)
  4. National Insurance Commission Solvency (2008)
  5. Saddlepoint approximations to the probability of ruin in finite time for the compound Poisson risk process perturbed by diffusion (2016)
  6. Ruin Theory Starter Kit (2013)
  7. On the expected discounted penalty function at ruin of a surplus process with interest (2002)
  8. Bounds for the ruin probability of a discrete-time risk process (2009)
  9. Developments in insurance mathematics (2001)
  10. Ruin estimates under interest force (1995)
  11. Ruin under interest force and subexponential claims: a simple treatment (2000)
  12. The transition from monopoly to competition: The case of housing insurance in Baden-W "u rttemberg (1996)
  13. Ruin probabilities with dependent claims (2002)
  14. A dependent frequency–severity approach to modeling longitudinal insurance claims (2019)
  15. Bayesian multivariate Poisson models for insurance ratemaking (2011)
  16. Aggregate claim models with one-way and two-way dependence among individual claims (2018)
  17. On the dependency of risks in the individual life model (1997)

0 of 25 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.