Risk Theory pp 35-46 | Cite as

Utility Theory

  • Hanspeter Schmidli
Part of the Springer Actuarial book series (SPACT)


We try to understand how agents take decisions. We assume that agents always act rationally and measure their wealth by a utility function. We determine the minimal premium an agent needs to take over a risk or the maximal premium an agent accepts to underwrite an insurance contract. We determine optimal insurance contracts. Finally, we study the sharing of risk such that no agent can improve his/her position without deteriorating the position of another.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of CologneCologneGermany

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