Optimal insurance demand under marked point processes shocks

Research output: Contribution to journalArticlepeer-review


We study the stochastic control problem of maximizing expected utility from terminal wealth, when the wealth process is subject to shocks produced by a general marked point process; the problem of the agent is to derive the optimal allocation of his wealth between investments in a nonrisky asset and in a (costly) insurance strategy which allows "lowering" the level of the shocks. The agent's optimization problem is related to a suitable dual stochastic control problem in which the constraint on the insurance strategy disappears. We establish a general existence result for the dual problem as well as the duality between both problems. We conclude by some applications in the context of power (and logarithmic) utility functions and linear insurance premium which show, in particular, the existence of two critical values for the insurance premium: below the lower critical value, agents prefer to be completely insured, whereas above the upper critical value they take no insurance.

Original languageEnglish (US)
Pages (from-to)283-312
Number of pages30
JournalAnnals of Applied Probability
Issue number1
StatePublished - Feb 2000


  • Convex analysis
  • Duality
  • Optimal insurance
  • Optional decomposition
  • Stochastic control

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Optimal insurance demand under marked point processes shocks'. Together they form a unique fingerprint.

Cite this