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## Two Competing Companies Insuring Multiple Objects

Following the model of previous section we will approximate discrete set of insurance policies by the continuous one and shall use similar expressions of the expected cumulative utility function of multiple customers.

The expected utilities of two competing insurance companies are defined as in the previous section.

|  |  | (34)

where is a probability of profit ,
is a utility of the profit .

Suppose that
.
From (26)

|  |  | (35)

where is a number customers that decided to insure their property at the company and shows how many of them survive.

From here and assumption (26) the probability of profit

|  |  | (36)

This defines the expected utility function for the insurance company .

Note that insurance policies are defined indirectly by the number of customers that insure their objects at the company . It is supposed that customers maximize expected cumulative utility that depends on the rates of insurance charges .

The equilibrium between interests of companies and customers is achieved if insurance policies and insurance charges satisfy Nash conditions. Here search for the Nash equilibrium is performed minimizing differences between the fraud and contract vectors.

Subsections

- Search for Equilibrium

Next: Search for Equilibrium Up: Nash Equilibrium Previous: Single Company Insuring Multiple