Stop-Loss Normal Approximation Expected Cost Calculator

Estimate the expected aggregate loss above an attachment point under a normal approximation, before expenses or risk loads.

Description

Estimate the expected aggregate loss above an attachment point under a normal approximation, before expenses or risk loads.

Stop-Loss Normal Approximation Expected Cost Calculator provides a focused, reproducible calculation with explicit inputs and a deterministic result. Estimate the expected aggregate loss above an attachment point under a normal approximation, before expenses or risk loads.

Use to approximate expected aggregate loss above an attachment when aggregate loss is modeled as normal.

When to use Stop-Loss Normal Approximation Expected Cost Calculator

Use to approximate expected aggregate loss above an attachment when aggregate loss is modeled as normal.1

How the calculation works

Estimate the expected aggregate loss above an attachment point under a normal approximation, before expenses or risk loads.2

E[(S−d)+] = σφ(z) + (μ−d)[1−Φ(z)]

Inputs and interpretation

Keep every input on the same valuation, timing, unit, and assumption basis. Interpret the output at the precision supported by those inputs rather than treating extra decimal places as additional certainty.

Limitations and assumptions

Normal loss models permit negative values and can understate skew or tail risk; the result is expected cost before expenses and risk loads, not a quoted premium.

References

  1. The Effect of Trend on Excess of Loss Coverage — Casualty Actuarial Society

  2. Actuarial science — Wikipedia contributors

Similar or alternative tools

Don't forget to set a bookmark for tool.io!
Privacy | Imprint | Cookies