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Mathematical model of prospect theory
Suppose that a person's mathematical function (PT function) to measure decision-making gains and losses is: u = ω (p1) v (X 1)+ω (p2) v (x2)+...+ω (pn) v (xn), where x1and x2. V is the so-called "value function", which represents the relative value of different possible outcomes in the minds of decision makers. According to this theory, the straight line of the value function should pass through the middle "reference point" to form an S-shaped curve as shown in the figure:

Its asymmetry shows that the absolute value of a loss result is greater than that of a profit result, that is, people have so-called "loss aversion" Different from the expected utility hypothesis, the method of measuring profit and loss in this theory does not consider "absolute wealth". Function w is a "probability weighted function" to express the general people's reaction to probability. Generally speaking, people will overreact to the extremely impossible and underreact to the medium and high possible.

Let's look at the actual operation of this theory-suppose a person is going to buy insurance, what will his decision be? Assume that the insured project has a 1% probability of distress; In case of distress, the loss of the insured is $65,438+0,000; And the premium is $ 15. Before applying the prospect theory, we should set a "reference point", which may be (1) the existing wealth or (2) the worst case, that is, the loss of $65,438+$0,000.

If the "existing wealth status" is taken as the reference point, the insured can pay the premium of 15 USD, and the "PT utility" is V (? 15), and his possible income is 0 dollars (99% probability), or -65438 dollars+0,000 dollars (1%probability). The total PT utility value will be: We can calculate the utility value according to the formula. If the general function is applied, the absolute value of the first term of the formula will be larger because V is convex when it is lost, which makes the overall PT utility value much smaller than V (? 15), and the return of buying insurance looks much smaller than not buying it. This means that the applicant will not buy insurance.

On the other hand, if the "loss of $65,438+0,000" is taken as the reference point, the utility value of PT will increase because of the concavity of V when it is profitable, and the result is greater than V (? 15), it seems that buying insurance is more attractive than not buying it.