Matematisk modellering KU

Hej, jeg læser matematik som tilvalgsfag på Københavns Universitet, og her i den forbindelse fået følgende opgave:

We want to study the personal decisions in taking an insurance against
theft at home.

(1) Formulate a mathematical model and find the solution: write down the decision tree with all
possible outcomes and utilities:

u1 the person does not take the insurance and a theft occurs
u2 the person does not take the insurance and a theft does not occur
u3 the person takes the insurance and a theft occurs
u4 the person takes the insurance and a theft does not occur

Find the expected probabilities of each outcome, as function of the probability of theft p and
the personal utilities u = (u1, u2, u3, u4). By comparing expected probabilities, when will a
person take the insurance?

(2) Interpret the solution: Using the model and further assumptions on how the personal utilities
would relate to the personal income I and the value of the items in the house V , explain how
the decision changes as I increases and as V increases. (Hint: observe that the decision only
uses the differences DELTA1 = u2 - u4 and DELTA2 = u3 - u1. Justify that these are positive).

(3) These differences on personal utilities depend on the price of the insurance Q in relation to I
and V . For p fixed, propose mathematical functions f, g such that
DELTA1 = f(Q, I, V ) DELTA2 = g(Q, I, V ).

Use this to propose a model for an insurance company in order to predict how many people
in a region would take the insurance as a function of its price (you can assume you know the
exact income and an estimation of the value in the house for all habitants in the region).

Jeg er fuldstændig på bar bund, da vi ikke rigtig har noget undervisningsmateriale udover slides fra forelæsninger. Er der nogen der har en ide til hvordan opgaven kan gribes an? :/

Mvh.