Pricing Insurance Risk. Stephen J. Mildenhall

Чтение книги онлайн.

2 The Insurance Market and Our Case Studies

      In this chapter, we outline the operation of the insurance market as we model it and describe the hypothetical Ins Co. used in our examples. We then introduce a Simple Discrete Example and three more realistic Case Studies which are used throughout the book to illustrate the methods presented in the theory chapters.

      2.1 The Insurance Market

      Insurers are one period, limited liability entities with no existing liabilities. We consider multi-period insurers in Part IV only. The insurer is called Ins Co. It sells insurance policies to insureds or policyholders. Policyholder and insured are treated as synonyms, and both include claimants. Ins Co.’s portfolio is the collection of policies it writes. The length of the period is usually one year. Its length is relevant only because of the time value of money, since interest is a rate per year.

      Policyholder liabilities are any amounts Ins Co. owes to policyholders. The two biggest are loss reserves and unearned premium reserves. We incorporate reserves in Part IV only. In property-casualty insurance, loss reserves cover claims that have been incurred but not paid, whether reported or not. In life insurance, liabilities include policy values for long duration contracts.

      Assets are the total financial resources owned by Ins Co. that it can use to meet its policyholder liabilities. A regulator usually stipulates required assets, a minimum amount of assets that Ins Co. must hold; see Section 1.2.

      Ins Co., like all firms, finances its assets by issuing liabilities. It sells policies, creating policyholder liabilities, in exchange for premiums, and it raises capital from investors by selling them its residual value (equity) or other promises (debt, reinsurance).

      Investors can be shareholders when Ins Co. is a stock company or insureds when it is a mutual company or debt holders or reinsurers.

      Insurers are intermediaries between insureds and investors. Intermediary always means an insurance company intermediary, and never an agent or broker.

Portfolio components are referred to as units. A unit can be a single policy or a group of policies or be defined by line, geography, branch, business unit, or other characteristics. Unit can also represent the segmentation between reinsurance ceded losses and retained losses.

      Ins Co.’s aggregate loss is the sum of losses from its portfolio over one period.

      Ins Co.’s operations are controlled by eight variables: (expected) loss, premium, assets, margin, capital, loss ratio, cost of capital, and leverage. The first five are monetary quantities, and the last three are unitless ratios. They obey five relationships:

Figure 2.1 lays out these variables and relationships. Monetary quantities are the vertices, the bold diagonal lines correspond to the ratios, and the two shaded triangles signify the asset and premium sum conditions.