Ruin Theory: When Do Insurance Companies Fail?

Insurance companies conduct business by underwriting future uncertainties. What happens if, in a specific period, accidents occur far more frequently than expected, exhausting the company’s funds (surplus)? Studying this phenomenon is the core of Ruin Theory.

1. The Surplus Process

An insurer’s surplus changes over time according to the following logic:

2. Factors Affecting the Probability of Ruin ($\psi$)

The probability of ruin is not just a matter of ‘luck’; it depends on the insurer’s management strategy.

• Initial Surplus ($u$): The more capital available at the start, the ruin probability decreases exponentially.
• Security Loading ($\theta$): The margin or markup added to premiums above the expected loss.
• Claim Volatility: Greater variance in the size of individual claims increases the risk of ruin.

3. Practical Analysis: Relationship Between Capital Size and Ruin Rate

The table below demonstrates how the ruin probability ($\psi$) changes as the initial capital ($u$) increases within a consistent risk environment.

💡 Professor’s Tip

Ruin Theory forms the basis for determining an insurer’s ‘Solvency Ratio.’ Regulations like the RBC ratio or K-ICS are essentially mechanisms to check, “Is the company managing its ruin probability below a certain threshold?”

🔗 Next Step

• Ch9: Reinsurance Structures