# please explain the definition of "common shock"?

i am reading a study manuel for the actuarial exam, Exam M. i have read up to the point where it mentions about "common shock model." i am so confused about the meaning of "common shock." if u no that, plz explain thoroughly what it means and how this model works.

Relevance

Say for instance you have joint-life coverage for a married couple. If the married couple is inseparable and they get into a car accident, there is a common shock element there.

This adds a dependent portion to the tPxy function for the couple.

Say both x,y follow constant force mortality models where x has a 0.04 factor, and y has a 0.05 factor.

tPx = e^-0.04t

tPy = e^-0.05t

tPxy = e^-0.09t

Now add in common shock with a constant force of 0.01

tPx* = e^-0.05t

tPy *= e^-0.06t

tPxy *= e^-0.10t

Now this isn't intuitive, but the shock causes a lack of independence and therefore tPxy is not equal to tPx*tPy. Now tPxy* = tPx*tPy*common shock

Just remember to not double count the common shock.

Good luck on that exam, I failed it a few times before I finally passed.