Optimal premium policy of an insurance firm: Full and partial information

Jianhui Huang, Guangchen Wang, Zhen Wu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

25 Citations (Scopus)

Abstract

Herein, we study the optimization problem faced by an insurance firm who can control its cash-balance dynamics by adjusting the underlying premium rate. The firm's objective is to minimize the total deviation of its cash-balance process to some pre-set target levels by selecting an appropriate premium policy. Our problem is totally new and has three distinguishable features: (1) both full and partial information cases are investigated here; (2) the state is subject to terminal constraint; (3) a forward-backward stochastic differential equation formulation is given which is more systematic and mathematically advanced. This formulation also enables us to continue further research in a generalized stochastic recursive control framework (see Duffie and Epstein (1992), El Karoui et al. (2001), etc.). The optimal premium policy with the associated optimal objective functional are completely and explicitly derived. In addition, a backward separation technique adaptive to forward-backward stochastic systems with the state constraint is presented as an efficient and convenient alternative to the traditional Wonham's (1968) separation principle in our partial information setup. Some concluding remarks are also given here.
Original languageEnglish
Pages (from-to)208-215
Number of pages8
JournalInsurance: Mathematics and Economics
Volume47
Issue number2
DOIs
Publication statusPublished - 1 Oct 2010

Keywords

  • Backward separation technique
  • Forward-backward stochastic differential equation
  • Optimal premium policy
  • Partial information
  • Stochastic control

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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