Sensitivity Analysis of Ruin Probability Considering Claim Dependence in a Ghanaian Insurance Company

Centrala begrepp

Calculating ruin probability based on the assumption of claim independence, while common, leads to underestimation when claims are actually dependent, especially for larger insurance companies and higher initial reserves.

Sammanfattning

• Bibliographic Information: Pabifio, D.T. (2024). Sensitivity Analysis of Ruin of an Insurance Company in Ghana. arXiv preprint arXiv:2410.11846v1.
• Research Objective: To conduct a comparative sensitivity analysis of ruin probability under both assumptions of claim dependence and independence using data from an insurance company in Ghana.
• Methodology: The study used secondary data from an insurance company in Ghana obtained from the National Insurance Commission (NIC) for the period of 2013 to 2017. Copulas were employed to determine claim dependence among various insurance products. Ruin probabilities were calculated at different start-up capitals under both dependence and independence assumptions. Statistical tests, including the Wilcoxon signed-rank test and the Friedman test, were used to compare the ruin probabilities under the two assumptions.
• Key Findings: The study found a significant positive relationship between the amount of claims paid and the number of claims recorded, indicating claim dependence. Ruin probabilities calculated under the assumption of claim dependence were consistently higher than those calculated under the assumption of independence. This difference became more pronounced with higher initial surplus values. Fire and Allied insurance exhibited the highest level of claim dependency among the insurance products studied.
• Main Conclusions: Assuming claim independence in ruin probability calculations leads to an underestimation of the actual risk, especially for larger insurance companies and as the initial reserves increase. The study recommends that insurance companies should incorporate claim dependence into their risk models to obtain more accurate ruin probability estimates.
• Significance: This research highlights the importance of considering claim dependence in ruin probability calculations for insurance companies. Accurately estimating ruin probability is crucial for insurance companies to determine appropriate reserve levels, manage risk effectively, and ensure solvency.
• Limitations and Future Research: The study was limited to data from a single insurance company in Ghana. Future research could expand the analysis to include multiple insurance companies from different geographical locations and investigate the impact of different types of copulas on ruin probability calculations.

Statistik

The mean and the standard deviation of the amount of claim paid per month were 365,932.23 and 365,356.78, respectively.
On average, the insurance company received a premium of 1,257,523.01, ranging from 766.06 to 4,087,163.02.
Motor Insurance recorded the highest rate of claims paid (ˆϑ = 0.000000573), followed by Fire and Allied (ˆϑ = 0.00000032).
Fire and Allied insurance recorded the highest level of dependency with a correlation coefficient (r = 0.891; p −value = 0.031) and a lower copula value (η = 0.031; p −value = 0.8003).

Citat

"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."
"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."

Viktiga insikter från

Sensitivity Analysis of Ruin of an Insurance Company in Ghana

by Daniel Tawia... på arxiv.org 10-17-2024

https://arxiv.org/pdf/2410.11846.pdf

Djupare frågor

How can regulatory bodies in the insurance industry encourage or enforce the adoption of claim dependence in ruin probability calculations by insurance companies?

Regulatory bodies can play a crucial role in promoting the use of more realistic ruin probability models that incorporate claim dependence. Here are some strategies:

Updated Solvency Regulations: Integrate claim dependence considerations into solvency capital requirements. This could involve:

Mandating Copula-Based Calculations: Require insurers to use copula methods or other suitable techniques for explicitly modeling dependencies between different risk categories (e.g., lines of business, geographic regions).
Stress Tests with Dependence: Design stress tests that simulate scenarios with correlated claims, reflecting potential real-world events like natural disasters or economic downturns.
Risk-Based Capital Charges: Adjust capital charges based on the level of dependence identified in an insurer's portfolio. Higher dependence could lead to higher capital requirements.

Data Collection and Sharing:

Standardized Data Templates: Establish standardized data reporting formats that facilitate the analysis of claim dependencies across the industry.
Industry-Level Data Pooling (Anonymized): Encourage the creation of anonymized industry-level databases of claims data. This would provide insurers with richer datasets to calibrate dependence structures in their models.

Guidance and Training:

Issue Best Practice Guidelines: Publish guidelines on appropriate methods for modeling claim dependence, including examples and case studies.
Provide Technical Support: Offer workshops and training programs to help actuaries and risk managers understand and implement dependence modeling techniques.

Supervisory Review Process:

Enhanced Model Validation: During the supervisory review of internal models, place greater emphasis on the validation of dependence assumptions.
Qualitative Assessment of Dependence: Incorporate a qualitative assessment of an insurer's approach to managing dependence risk as part of the overall solvency assessment.

Could the underestimation of ruin probability due to the assumption of claim independence be mitigated by other risk management strategies employed by insurance companies?

While incorporating claim dependence directly into ruin probability calculations is essential, other risk management strategies can partially mitigate the risks associated with underestimation:

Diversification:

Across Lines of Business: Offering a wider range of insurance products that are not highly correlated can reduce the impact of a single event causing a large number of claims.
Geographic Diversification: Spreading risk across different geographic regions can mitigate the impact of localized events.

Reinsurance:

Tail Risk Coverage: Purchasing reinsurance, particularly for tail risks (extreme events), can provide a financial buffer in case of unexpectedly large or correlated claims.
Treaty Reinsurance with Dependence Considerations: Structure reinsurance treaties that explicitly account for potential claim dependencies.

Conservative Reserve Setting:

Actuarial Prudence: Employing conservative assumptions in actuarial models, even when assuming independence, can create a larger safety margin.
Sensitivity Analysis: Regularly conducting sensitivity analyses on reserve estimates, varying the degree of assumed correlation, can provide insights into potential shortfalls.

Investment Policy:

Matching Asset-Liability Profile: Aligning the investment portfolio's duration and risk characteristics with the expected timing and potential correlation of claims can reduce the impact of adverse market movements coinciding with large claim payouts.

Underwriting Standards:

Risk Selection and Pricing: Rigorous underwriting standards, including careful risk selection and adequate pricing for correlated risks, are crucial.
Important Note: These strategies can help reduce the overall risk exposure, but they are not a substitute for explicitly modeling claim dependence in ruin probability calculations.

How can the insights from ruin theory be applied to other industries or fields that face similar challenges of managing risk and uncertainty?

The core principles of ruin theory, which focuses on the probability of a company's financial reserves being depleted due to unexpected events, have broad applicability beyond insurance:
1. Finance and Investment Management:

Hedge Fund Risk: Assessing the risk of substantial losses or fund closure due to correlated market movements.
Portfolio Optimization: Incorporating dependence structures between assets to construct more robust portfolios.
Credit Risk Modeling: Evaluating the likelihood of defaults on loans, considering potential correlations between borrowers.
2. Operations Research and Supply Chain Management:

Inventory Control: Determining optimal inventory levels while accounting for the risk of supply chain disruptions due to correlated events (e.g., natural disasters, geopolitical instability).
Project Management: Assessing the probability of project failure due to delays in interdependent tasks, considering potential correlations in task durations.
3. Healthcare and Epidemiology:

Hospital Capacity Planning: Modeling the probability of hospitals exceeding capacity due to surges in demand, particularly during pandemics with correlated infection rates.
Spread of Infectious Diseases: Simulating the spread of diseases, taking into account factors like social networks and population density that can lead to correlated infection patterns.
4. Environmental Science and Climate Change:

Extreme Weather Events: Modeling the probability of catastrophic events like floods, droughts, or wildfires, considering the increasing frequency and potential correlation of such events due to climate change.
Ecosystem Collapse: Assessing the risk of ecosystem collapse due to interconnected species dependencies and the potential for cascading failures.
Key Adaptations:

Nature of "Ruin": The definition of "ruin" needs to be tailored to the specific context. In finance, it might be bankruptcy; in project management, project failure.
Data Availability: The availability of relevant data to calibrate dependence structures is crucial.
Model Complexity: The complexity of the models used should be balanced with the interpretability of results and the computational resources available.