Ӧ�ø���ͳ�� 2013, 29(6) 642-654 DOI:      ISSN: 1001-4268 CN: 31-1256

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�ؼ����� PDS   ��Ԫ���ϲ���ģ��   �����ٱ���   ���Ӻ���.  
Optimal Reinsurance with Risks Positively Dependent through the Stochastic Ordering
Zhang Jiesong, Xiao Qingxian
Business School, University of Shanghai for Science and Technology; School of Mathematical Sciences, Huaibei Normal University
Abstract:

In the classic bivariate compound Poisson
models, the numbers of claims are assumed to be correlated through a
common Poisson distribution, while the claim sizes are independent.
In this paper, we assume that both the numbers of claims and claim
sizes are positively dependent through the stochastic ordering.
Through comparing, we find that the condition of positive dependence
through the stochastic ordering is weaker than correlating
through a common Poisson distribution. In fact, the assumption of
positive dependence through the stochastic ordering is weaker than
independence, comonotonicity, conditionally stochastically
increasing et al.. With the positively dependent risks through the
stochastic ordering, we get the optimal reinsurance strategy. In
addition, with the mixed two-dimensional and stochastic-dimensional
dependent risks, we give the explicit expressions of retention
vector under the criterion of minimizing the variance of the total
retained loss and maximizing the quadratic utility, which partially
solves the problem, proposed by Cai and Wei (2012a), of getting such
expressions with multi-dimensional dependent risks.

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