Keywords: sharesl

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## Single Company Insuring Single Object

In this section the optimal insurance is regarded as a problem of insurance company. We start from the simplest case of single company insuring a single object.

The expected utility of this object

|  |  | (17)

where is a probability of wealth ,
is an utility function of the wealth .
Here is the rate of insurance charge.

Suppose that
and

|  |  | (18)

Here is the market value of the object,
the product denotes insurance charge of the object.
is insurance policy of the object.
, if the object survives,
, if not.
is a survival probability of the object.

The expected utility of the insurance company

|  |  | (19)

where is a probability of profit ,
is an utility function of the profit .
Suppose that
and

|  |  | (20)

Here insurance policy is defined by the owner of object which maximizes his utility (15) depending on the rate of insurance charge . The equilibrium between interests of the company and the customer is achieved when both insurance policy and insurance charge satisfies Nash conditions.

Subsections

- Search for Equilibrium

Next: Search for Equilibrium Up: Nash Equilibrium Previous: Nash Equilibrium