By Boelviken E.
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Additional info for Computation and Modelling in Insurance and Finance
5 for a simple model. There have been attempts to determine γ from theoretical arguments, see Young (2004) for a review, but these eﬀorts are not used much in practice and will not be considered. The loading concept separates the market side from the insurance process itself, but another issue is whether the pure premium is known. Stochastic models for X always depend on unknown quantities such as parameters or probability distributions. They are determined from experience or even assessed informally if historical data are lacking, and there is a crucial distinction between the true πpu with perfect knowledge of the underlying situation and the πˆ pu used for analysis and decisions.
Another possibility is ak = 1 + r where r is a rate of interest, and now Y1 , Y2 , . . are values of an account influenced by random input. 24) and two diﬀerent sources of risk that might themselves demand extensive modelling and simulation are integrated. 6. Here the target is a more modest one. A simple Monte Carlo algorithm and notation for such schemes will first be presented and then four simple examples. The aim is to introduce a general line of attack and indicate the power of Monte Carlo for problem solving, learning and communication.
The second version based on 1 − U is due to U and 1 − U having the same distribution. 1 Sampling by inversion 0 Input: The percentile function F −1 (u) 1 Draw U ∗ ∼ uniform 2 Return X ∗ ← F −1 (U ∗ ) or X ∗ ← F −1 (1 − U ∗ ). pair with a speed-enhancing potential to be discussed in Chapter 4. 1 is practical depends on the ease with which the percentile function F −1 (u) can be computed. 5. 3 Acceptance–rejection Acceptance–rejection is a random stopping rule and much more subtle than inversion.