RESEARCH ARTICLE

VaR Criteria for optimal limited changeloss and truncated change-loss reinsurance

  • Xiaojing MA , 1 ,
  • Lan WU 1,2
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  • 1. Department of Financial Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China
  • 2. Center for Statistical Science, Peking University, Beijing 100871, China

Received date: 04 Apr 2012

Accepted date: 12 Dec 2012

Published date: 01 Jun 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

Reinsurance can provide an effective way for insurer to manage its risk exposure. In this paper, we further analyze the optimal reinsurance models recently proposed by J. Cai and K. S. Tan [Astin Bulletin, 2007, 37(1): 93-112]. With the criteria of minimizing the value-at-risk (VaR) risk measure of insurer’s total loss exposure, we derive the optimal values of sharing proportion a, retention d, and layer l of two reinsurance treaties: the limited changeloss f(x) = a{(x - d)+ - (x - l)+} and the truncated change-loss f(x) = a(x-d)+I(xl). Both of the reinsurance plans have been considered to be more realistic and practical in the real business. Our solutions have several appealing features: (i) there is only one condition to verify for the existence of optimal limited change-loss reinsurance while there always exists an optimal truncated change-loss reinsurance, (ii) the resulting optimal parameters have simple analytic forms which depend only on assumed loss distribution, reinsurer’s safety loading, and insurer’s risk tolerance, (iii) the optimal retention d for limited change-loss reinsurance is the same as that by Cai and Tan while the optimal value is smaller for truncated change-loss, (iv) the optimal sharing proportion and layer are always the same for both reinsurance plans, (v) minimized VaR are strictly lower than the values derived by Cai and Tan, (vi) the optimization results reveal possible drawbacks of VaR-based risk management that a heavy tail risk exposure may be expressed by lower VaR.

Cite this article

Xiaojing MA , Lan WU . VaR Criteria for optimal limited changeloss and truncated change-loss reinsurance[J]. Frontiers of Mathematics in China, 2013 , 8(3) : 583 -608 . DOI: 10.1007/s11464-013-0278-x

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