Property Coinsurance

Property insurance frequently contains a "coinsurance clause" stating that, if the insured values its property at some fraction

of its actual value

, and

is less than a coinsurance percentage

(often 80%), the insurer may reduce its payment to

of the loss. This Demonstration permits exploration of work done by Itzhak Venezia comparing an insurance policy with valuation α and coinsurance percentage

to an insurance policy with no coinsurance and a valuation percentage

, where

. The user sets

, and

with sliders and sets the parameters of the (beta) loss distribution function with a 2D slider. Mathematica outputs graphs showing insurance payments and wealth as a function of loss and a graph showing the cumulative distribution of wealth under both insurance policies.

Contributed by: Seth J. Chandler

Show Initialization Code

(30 lines omitted)

The policies will have the same premium if the areas under the curves in the bottom-most wealth distribution graphic are equal to each other. Assuming that the insured is risk averse and the premiums for the policies are the same, the insured will prefer the less "disperse" wealth distribution curve, which ends up always being the curve generated by an insurance policy with a coinsurance requirement. Professor Venezia's original article setting forth this model may be found in The Journal of Risk and Insurance, 55(2) 1988 pp. 307-314. The graphics go black if the constraint

is violated.

The top panel contains an inset identifying the fraction of property value insured when coinsurance is present that will cost the insured the same premium as the policy with a lower fraction of property value insured but without coinsurance. The policy with coinsurance will yield a risk averse insured greater utility than the equally priced policy without coinsurance.

Snapshot 1: a different loss distribution function and a low coinsurance requirement

Snapshot 2: the same loss distribution function as in Snapshot 1 but with a high coinsurance requirement and low α

Snapshot 3: a loss distribution function with a high first parameter and low second parameter