MCPCalc

Risk & Ruin Probability Calculator

Estimate insurer ruin probability bounds using a Cramer-Lundberg model with Poisson claims and exponential severity.

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What This Calculator Does

Estimate insurer ruin probability bounds using a Cramer-Lundberg model with Poisson claims and exponential severity.

It combines Initial Surplus, Premium Rate (per period), Claim Frequency λ (per period), Mean Claim Severity μ to estimate Lundberg Upper Bound on Ruin, Approximate Ruin Probability, Adjustment Coefficient (R).

Formula & Method

Core equations: Expected claim outflow is \lambda \mu where \lambda is claim frequency and \mu is mean claim severity. Net profit condition is c > \lambda \mu. For exponential claims, an adjustment coefficient is R = \frac{1}{\mu}\left(1 - \frac{\lambda\mu}{c}\right) when the net profit condition holds. Lundberg inequality gives ruin bound \psi(u) \le e^{-Ru}.

Notation used in the formulas: R = Lundberg Upper Bound on Ruin; x_{1} = Initial Surplus; x_{2} = Premium Rate (per period); x_{3} = Claim Frequency λ (per period); x_{4} = Mean Claim Severity μ.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Inputs Used

  • Initial Surplus: Used directly in the calculation.
  • Premium Rate (per period): Used directly in the calculation.
  • Claim Frequency λ (per period): Used directly in the calculation.
  • Mean Claim Severity μ: Used directly in the calculation.

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