Copulas在尾部風險值之模擬與計算

Simulation Study on Tail Value at Risk with Copulas

鄧秋鈺(Ciou-Yu Deng)

指導教授 ： 吳建華

中原大學/理學院/應用數學研究所/碩士(2010年)

https://doi.org/10.6840/cycu201000464

摘要

摘要
本篇論文主要是探討保險公司必須提供最低的償付能力額度，也就是所謂準備金的部分。當準備金提存的越多，保險公司之償付能力相對的越高，其資金調動的額度就越低，因此提存準備金的多寡對於保險公司的營運來說是最重要的一環。
在既定的信賴水準下，準備金是使用尾部風險值(tail value at risk)估計得來，同時估計殘餘風險(residual risk)的期望值與標準差。因險種之各保險項目彼此間是屬於不獨立的結構型態，所以我們使用copulas 模型配合不同的邊際分配估計準備金所需的額度。考量歷史資料的不足而低估尾部風險值，因此本篇以模擬的方式隨機抽取，以得到近實際資料的分佈。
本研究可知，保險公司之管理心態越趨保守下，其預提存的準備金應相對的提高，估計能力也較佳；另外，若某險種之兩保險項目相關性越大，當發生保險事故時，理賠金額也越高，其保險公司須提存之準備金相對的也增加。

關鍵字

風險值 ； 尾部風險值 ； 殘餘風險 ； copulas

並列摘要

ABSTRACT
In this paper, we focus on the required solvency level of an insurance company,which is the reserve.When keeping a large reserve, the solvency level of an insurance company is relatively higher, and the ability of funds transfer is lower. Keeping the amount of reserve is the most important issue for an insurance company.
The reserve is estimated by the tail value at risk in the α level , simultaneously, the mean and the variance of the residual risk are computed. Because insurance items of insurance are dependent, we use copulas model with different marginal distributions to estimate the reserve amount. Since the historical data is not enough to estimate the tail value at risk, we use the way of simulation in random to approximate the distribution of the actual data.
If the management of insurance company is more conservative, the reserve will be higher and the estimator will be better. In addition, if the correlation between two insured items is higher, the insurance company needs the adjustment amount and the reserve when the insurance accidence occurred.

並列關鍵字

copulas ； value at risk ； tail value at risk ； residual risk

參考文獻

Helder, P. P., Luin, K. H., 2006,“Using Conditional Copula to Estimate Value at

江昱霖, 2007,“The Study of Safety-First Portfolio Optimization Problem under

曾毅豪, 2007,“Copulas for Risk Management in Financial Market.”, Department

of Statistics, National Cheng Kung University, master thesis.

Economics, National Central University, master thesis.