Skip to main content

Optimal reinsurance: a reinsurer’s perspective

  • Fei Huang (a1) and Honglin Yu (a1)

In this paper, the optimal safety loading that the reinsurer should set in the reinsurance pricing is studied, which is novel in the literature. It is first assumed that the insurer will choose the form of the reinsurance contract by following the results derived in Cai et al. Different optimality criteria from the reinsurer’s perspective are then studied, such as maximising the expectation of the profit, maximising the utility of the profit and minimising the value-at-risk of the reinsurer’s total loss. By applying the concept of comonotonicity, the problem in which the reinsurer is facing two risks with unknown dependency structure is also solved. Closed-form solutions are obtained when the underlying losses are zero-modified exponentially distributed. Finally, numerical examples are provided to illustrate the results derived.

Corresponding author
*Correspondence to: Fei Huang, Research School of Finance, Actuarial Studies and Statistics, College of Business and Economics, Australian National University, Canberra, ACT 2601, Australia. E-mail:, Phone: +61 2 61257390.
Hide All
Arrow, K.J. (1963). Uncertainty and the welfare economics of medical care. American Economic Review, 53, 941973.
Bernard, C. & Tian, W. (2009). Optimal reinsurance arrangements under tail risk measures. Journal of Risk and Insurance, 76(3), 709725.
Borch, K. (1960). An attempt to determine the optimum amount of stop loss reinsurance. Transactions of the 16th International Congress of Actuaries, 1, 597–610.
Cai, J. & Tan, K.S. (2007). Optimal retention for a stop-loss reinsurance under the VaR and CTE risk measures. ASTIN Bulletin, 37, 93112.
Cai, J., Tan, K.S., Weng, C. & Zhang, Y. (2008). Optimal reinsurance under VaR and CTE risk measures’. Insurance: Mathematics and Economics, 43(1), 185196.
Cheung, K.C. (2006). Optimal portfolio problem with unknown dependency structure. Insurance: Mathematics and Economics, 38(1), 167175.
Cheung, K.C. (2010). Optimal reinsurance revisited – a geometric approach. ASTIN Bulletin, 40, 221239.
Cheung, K., Sung, K., Yam, S. & Yung, S. (2014). Optimal reinsurance under general law-invariant risk measures. Scandinavian Actuarial Journal, 2014(1), 7291.
Chi, Y. & Lin, X.S. (2014). Optimal reinsurance with limited ceded risk: a stochastic dominance approach. ASTIN Bulletin: The Journal of the International Actuarial Association, 44, 103126.
Dhaene, J., Denuit, M., Goovaerts, M.J., Kaas, R. & Vyncke, D. (2002). The concept of comonotonicity in actuarial science and finance: theory’. Insurance: Mathematics and Economics, 31(1), 333.
Guerra, M. & Centeno, M. (2008). Optimal reinsurance policy: the adjustment coefficient and the expected utility criteria. Insurance: Mathematics and Economics, 42(2), 529539.
Panjer, H.H. & Willmot, G.E. (1992). Insurance Risk Models. Society of Actuaries, Schaumburg, Illinois, United States.
Tan, K.S., Weng, C. & Zhang, Y. (2011). Optimality of general reinsurance contracts under CTE risk measure. Insurance: Mathematics and Economics, 49(2), 175187.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Annals of Actuarial Science
  • ISSN: 1748-4995
  • EISSN: 1748-5002
  • URL: /core/journals/annals-of-actuarial-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 17
Total number of PDF views: 72 *
Loading metrics...

Abstract views

Total abstract views: 362 *
Loading metrics...

* Views captured on Cambridge Core between 4th September 2017 - 17th March 2018. This data will be updated every 24 hours.