Constant-loss limit of a normal risk calculation

Use an original constant loss

If mean loss is 7 and dispersion is zero, the model loss is always 7. Every supported confidence gives VaR 7 and selected-tail average 7. The loss can also be a negative constant under a gain convention.

Avoid dividing by zero

The positive-dispersion normal density divides by σL, and standardized loss uses (L−μL)/σL. Neither expression is defined at σL=0. Treat the input as a constant-loss limit instead of attempting to draw a normal density.

Read the boundary behavior

Keep a stated model separate from certainty

Entering zero dispersion stipulates a constant law; it does not establish that a real exposure has no uncertainty. An estimated zero from a short or incomplete record needs its own data review.