Risk Theory

1. Front Matter

   Pages i-xvii

   PDF

2. Definitions and notation

   • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen

   Pages 1-17

3. Claim number process

   • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen

   Pages 18-46

4. Compound Poisson process

   • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen

   Pages 47-125

5. Applications related to one-year time-span

   • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen

   Pages 126-170

6. Variance as a measure of stability

   • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen

   Pages 171-182

7. Risk processes with a time-span of several years

   • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen

   Pages 183-257

8. Applications related to finite time-span T

   • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen

   Pages 258-287

9. Risk theory analysis of life insurance

   • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen

   Pages 288-307

10. Ruin probability during an infinite time period

    • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen

    Pages 308-318

11. Application of risk theory to business planning

    • Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen

    Pages 319-348

12. Back Matter

    Pages 349-408

    PDF

The theory of risk already has its traditions. A review of its classical results is contained in Bohlmann (1909). This classical theory was associated with life insurance mathematics, and dealt mainly with deviations which were expected to be produced by random fluctua­ tions in individual policies. According to this theory, these deviations are discounted to some initial instant; the square root of the sum of the squares of the capital values calculated in this way then gives a measure for the stability of the portfolio. A theory constituted in this manner is not, however, very appropriate for practical purposes. The fact is that it does not give an answer to such questions as, for example, within what limits a company's probable gain or loss will lie during different periods. Further, non-life insurance, to which risk theory has, in fact, its most rewarding applications, was mainly outside the field of interest of the risk theorists. Thus it is quite understandable that this theory did not receive very much attention and that its applications to practical problems of insurance activity remained rather unimportant. A new phase of development began following the studies of Filip Lundberg (1909, 1919), which, thanks to H. Cramer (1926), e.O.

• Finite
• Monte Carlo method
• Poisson process
• Simula
• Statistica
• business plan
• character
• computation
• distribution
• normal distribution
• programming
• simulation
• statistics
• stochastic processes
• system

• Leicestershire, England

  Robert Eric Beard

• Helsinki, Finland

  Teivo Pentikäinen, Erkki Pesonen

Policies and ethics