Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis

TL;DR

This paper analyzes an optimal reinsurance strategy to minimize the probability of drawdown in a risk model, demonstrating convergence to a diffusion approximation and establishing the strategy's near-optimality.

Contribution

It extends previous work by providing asymptotic analysis of the minimum drawdown probability under mean-variance premium principle, including convergence rates.

Findings

Minimum drawdown probability converges to that of the diffusion approximation.

Optimal strategy from the diffusion approximation is nearly optimal in the classical risk model.

Convergence rate of the probability is of order O(n^{-1/2}).

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.