Abstract
The last decades have seen the areas of insurance mathematics and mathematical finance coming closer together. One reason is the growing linking of pay-outs of life insurances and pension plans to the current value of financial products, another that certain financial products have been designed especially to be of interest for the insurance industry (see below). Nevertheless, some fundamental differences remain, and the present section aims at explaining some of these, with particular emphasis on the principles for pricing insurance products, resp. financial products.
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Notes
- 1.
The meaning of a 2 < 0 is simply that − a 2 is borrowed from the bank, whereas a 1 < 0 means that the investor has taken the obligation to deliver a volume of − a 1 stocks at time T = 1 (shortselling).
- 2.
Note that w 0 units of money at time 0 has developed into w 0er units at time 1 if put in the bank. Therefore, the fair comparisons of values is the ordering between e−rw 1 and w 0, not between w 1 and w 0.
- 3.
For example, if d > er, an arbitrage opportunity is to borrow from the bank and use the money to buy the stock.
- 4.
We do not explain the reasons for this requirement here!
- 5.
In the physics literature, p is usually implicitly specified through the half life T 1∕2 of an atom, that is, the median of its lifetime, which we will later see to be exponential, say at rate μ. This implies \({\mathrm {e}}^{-\mu T_{1/2}}\,=\,1/2\) and p = 1 −e−μ. For 238U, one has T 1∕2 = 4.5 × 109 years.
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Asmussen, S., Steffensen, M. (2020). Chapter I: Basics. In: Risk and Insurance. Probability Theory and Stochastic Modelling, vol 96. Springer, Cham. https://doi.org/10.1007/978-3-030-35176-2_1
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DOI: https://doi.org/10.1007/978-3-030-35176-2_1
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