Optimal insurance with background risk: An analysis of general dependence structures

Yichun Chi, Wei Wei

Research output: Contribution to journalArticlepeer-review


In this paper, we consider an optimal insurance problem from the perspective of a risk-averse individual who faces an insurable risk as well as some background risk and wants to maximise the expected utility of his/her final wealth. To reduce ex post moral hazard, we follow Huberman et al. (Bell J. Econ. 14:415–426 1983) to assume that alternative insurance contracts satisfy the principle of indemnity and the no-sabotage condition. When the insurance premium is calculated by the expected value premium principle, a necessary and sufficient condition for the optimality of an insurance contract is established under a general dependence structure between insurable and background risks. By virtue of this condition, some qualitative properties of optimal contracts are developed, a scheme is provided to improve any suboptimal insurance strategy, and optimal insurance forms are derived explicitly for some dependence structures of interest. These forms are not always piecewise linear.

Original languageEnglish (US)
Pages (from-to)903-937
Number of pages35
JournalFinance and Stochastics
Issue number4
StatePublished - Oct 1 2020
Externally publishedYes


  • Background risk
  • General dependence structures
  • Mossin’s theorem
  • No-sabotage condition
  • Optimal insurance design

ASJC Scopus subject areas

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty


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