Joining insured groups: how to split the emerging profit

  • Received May 14, 2017;
    Accepted September 30, 2017;
    Published November 24, 2017
  • Author(s)
  • DOI
    http://dx.doi.org/10.21511/ins.08(1).2017.03
  • Article Info
    Volume 8 2017, Issue #1, pp. 29-33
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In the process of evaluating the premium of an insurance plan, one considers the risk arising from various uncertainties. The authors suppose for a plan whose net premium is p and the standard deviation is σ the premium including the risk factor will be p + 3σ for a given member, and reflects the risk. For a group of n members with the same premium p and with standard deviation σ, the premium including the risk factor will be p + 3σ/√n where 3σ/√n reflects the risk for each member of the group. The authors study the emerging profit in case of n insured groups each with its own premium and its own risk when all the n insured groups merge into a single group uniting all insured members. They prove that there emerge a profit due to joining the n groups into a single one due to a reduced total risk of the n separate insured groups when merging into a single group. The emerging profit between the various groups may be divided using the Shapley values method or using utility functions for each group. The auhors discuss various reasonable ways to split the emerging profit between the n groups and show that the split of the profit depends on the chosen method. The main tools are techniques of game theory, in particular those of cooperative games.

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    • Table 1. Examples of merging