Insurance Formules Flashcards
(23 cards)
How to calculate the certainty equivalent with a formulae
Luigi’s utility with insurance equals:
U= (wealth –AFP- certainty equivalent)0.5 = (100 –50 – certainty equivalent)0.5
Luigi’s utility without insurance equals:
= 0.5* (wealth without being ill)0.5 + 0.5 (wealth if he gets ill)0.5
= 0.5* (100)0.5 + 0.5 (0)0.5
= 5
Solve the equation: U(insured) = U(uninsured)
Compute first Luigi’s expected wealth and the expected utility of his expected wealth:
Stap 1: expected wealth x kans op niet zoek +kans op ziek x expected wealth-zorgkost= 5
Expected wealth = 0,5 *100 + 0,5 (100-100) = 50 => U(50) = 5
Stap 2 : ga naar de grafiek en kijk bij nut en volg welk bedrag er bij hoort op de x as
What is the formulae for expected loss
Kans ziek x zorgkost + kans op niet ziek x zero= zorgkost
Formulae expected wealth
Kans ziek x wealth-zorgkost ) + (kans niet ziek x wealth),
How to calculate the expected utility
Kans ziek x wortel van wealth -zorgkost ) + kans niet ziek x wortel uit wealth = expected utility
What can you do with the utility
You can calculate the maximum premie he wants to pay
What is the formulae to calculate the maximum premie someone wants to pay
Utility = wealth - maximum premie ( hier de wortel van)
Utility x utility om de wortel rechts kwijt te raken
Dit bedrag minus de wealth geeft de maximum premie die iemand wil betalen.
How to calculate which probability “p” of having health care costs the insurer will have losses?
The maximum premie you calculated divided by the zorgkosten
Tot Wanneer is het gunstig voor een verzekerde om een zorgverzekering afte sluiten
Wanneer het nut van verzekering gelijk is aan het nut zonder verzekering.
Hoe bereken je het verwachte nut adh van een afp
Stel de afp is 80 dan ga. Je kijken in de grafiek 100-80 =20. Volg de lijn naar boven ( zie werkcollege) en lees het nu af, in dit geval is het 4.
What do you do when they ask : compute the maximum premium fred wants to pay for insurance
Wealth is 5000
Kans op ziek worden is 10%
Zorgkosten is 3000
Dit is de certainty equivalent :you compute the utility with insurance and the utility without insurance
Dus
Met verzekering wortel uit 5000-max premium=
Zonder verzekering = de kans op niet ziek worden plus de sortel uit wealth=0,90xwortel uit 5000+ de kans op ziek worden maar de wortel uit wealth-zorgkost
=getal rechts van de vergelijking quadrateren en aftrekken van de wealth ,dan krijg je de max premie
Max premie is dus 361
Wat gebeurd er als de verzekeraar meer vraagt dan 361 euro.
Hij zal zich niet verzekeren omdat zijn nut hoger is als hij NIET verzekerd is
Main questions for a insurance company: How can the health insurance company organize the finance of the health care optimal? Limitations during this proces:
One party (agent) is expected to act in another’s (principal) best interest”, but agent’s own best interest may differ from the principal’s best interest. (Information a symmetry).
So the insurance company needs to think about the price that he is going to ask of a premium to a insure. Wich treatments are covert?
What is the difference between supply induced demand and supply induced moral hazard
Supply-induced demand; The doctor has some time left so he will treat some more patient. And the patient has not the same information as the doctor.
Supply induced moral Hazard; Based on insurance the doctor will use extra care that is reimbursed.
What is ex ante moral hazard
Ex-post moral hazard; There is some care left for the patient so he will use them all.
How to detect if the utility with premie is higher/lower then utility without premie
Uitleg
What is the definition of the afp
the premium which is equal to the expected payments of the insurance company.
What is the certainty equivalent
Is the administration cost,moral hazard kost,profit from insurance.
Afp+ ce is the maximum premie
How do you see in the graph if someone is risk avers
His utility function is concave => the utility that Luigi will get from a certain amount of money is higher than the utility he will get from the same expected amount of money.
How can you compute a certainty equivalent
Compute first The expected wealth and the expected utility of his expected wealth: dus de wortel van we wealth nemen
Then go to the graph and see which amount of money belongs with that utility
What is the name of the premium that all insured have to pay and which is unrelated to their risk-profile?
Nominal premium
Wat zijn de nadelen van deductible,coinsurance en copayement.
Deductible has no effect anymore on the demand for care as soon as the patient has more health care expenses than the deductible. (unfair for chronic patients)
Co payment: does not work well with expensive care, and may still limit the access to care for individuals with low SES.
Coinsurance: may limit the access to care for individuals with lower SES.
What do you do if they say : show wether anna wants to purchase insurance or not.
Ok then you calculate the utility with insurance= utility without insurance. Dus niet de max premie maar de utility vergelijken.
