Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis
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SIAM Journal on Financial Mathematics
Abstract
In this paper, we consider an optimal reinsurance problem to minimize the probability of drawdown
for the scaled Cram´er-Lundberg risk model when the reinsurance premium is computed
according to the mean-variance premium principle. We extend the work of Liang et al. [16] to
the case of minimizing the probability of drawdown. By using the comparison method and the
tool of adjustment coefficients, we show that the minimum probability of drawdown for the scaled
classical risk model converges to the minimum probability for its diffusion approximation, and the
rate of convergence is of order O(n−1/2). We further show that using the optimal strategy from
the diffusion approximation in the scaled classical risk model is O(n−1/2)-optimal
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Keywords
Optimal reinsurance, Probability of drawdown, Scaled Cram´er-Lundbergmodel, Asymptotic analysis, Diffusion approximation