Calculating insurance in Risk Management I have a scenario.... A House is worth $200,000 chance of burning down accidentally each year p = 0.001 (1/100000) threat of flooding accidentally each year p = 0.0001 (1/1000000) Question is "What should we pay to insure the house, if either a flood or fire will destroy the house completely?" My calcuation is: considering if we want to be able to buy a house with same value, $200,000* 0.999 (no-accident) + $200,000*0.001 (burning accident) - insurance = $200,000 - insurance Insurance value should be $200 or less. ($200 = $200,000*0.001) Appreciate if someone can advise if this make sense. Thanks.

If either a fire or flood occurs, the value of the house is zero. Thus, the expected value $EV$ of the house is given by $$EV=200,000(1-p_{flood})(1-p_{fire})+0p_{flood}(1-p_{fire})+0p_{fire}(1-p_{}flood)+0p_{flood}p_{fire}$$ $$=200,000(1-p_{flood})(1-p_{fire})$$ $$=200,000(1-0.001)(1-0.0001)$$ which is $199,780.02$.

Now, $EV$ must be equal to the replacement cost $RC$ of the house minus the cost to insure $CI$ the house.

Thus, $EV=RC-IC$, which implies the $IC=RC-EV=200,000=199,780.02=219.98$.