Consider a risk model in which X₁,…, X_n are n potential losses from different risky assets at the terminal time, and ${\theta }_1,\dots ,{\theta }_n$ are n discount factors over the period. In this paper, we establish some asymptotic formulas for the value at risk and conditional tail expectation of the total discounted loss $S_n={\sum }_{i=1}^n{\theta }_i{X}_i$ of an investment portfolio. We also demonstrate our obtained results through Monte Carlo simulations with asymptotics.

中文翻译：

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具有风险价值的渐近性和投资组合损失的有条件尾部期望

考虑一个风险模型，其中X ₁，…，  X _n是终端时间不同风险资产的n个潜在损失，并且${\theta }_{\mathrm{1个}}，\dots ，{\theta }_{ñ}$在此期间是n个折现因子。在本文中，我们为总折现损失的风险价值和条件尾部期望建立了一些渐近公式${\mathrm{小号}}_{ñ}={\sum }_{\mathrm{一世}=\mathrm{1个}}^{ñ}{\theta }_{\mathrm{一世}}{X}_{\mathrm{一世}}$投资组合。我们还通过渐近的蒙特卡洛模拟证明了我们获得的结果。