Bounding Contingent Claim Prices via Hedging Strategy with Coherent Risk Measures
Bounding Contingent Claim Prices via Hedging Strategy with Coherent Risk Measures
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DOI：
10.1007/s10957-011-9899-y
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发表时间：
2011-08
影响因子：
1.9
通讯作者：
Jun-ya Gotoh;Yoshitsugu Yamamoto;Weifeng Yao
中科院分区：
文献类型：
--
作者：
Jun-ya Gotoh;Yoshitsugu Yamamoto;Weifeng Yao
我们推广了基于一致风险测度的套利概念，并研究了一种数学优化方法，用于收紧不完全市场中未定权益价格的上下界。由于一致性风险度量的对偶表示，通过求解一对半无限线性优化问题来确定价格的上下界，当使用条件风险价值（CVaR）作为风险度量时，这一问题进一步归结为线性优化问题.我们还表明，套期保值投资组合问题被视为一个强大的优化问题。调整参数的风险度量，我们证明了数值例子，这两个界限的方法彼此和收敛到一个价格，这是公平的意义上，卖方和买方面临相同的风险。
We generalize the notion of arbitrage based on the coherent risk measure, and investigate a mathematical optimization approach for tightening the lower and upper bounds of the price of contingent claims in incomplete markets. Due to the dual representation of coherent risk measures, the lower and upper bounds of price are located by solving a pair of semi-infinite linear optimization problems, which further reduce to linear optimization when conditional value-at-risk (CVaR) is used as risk measure. We also show that the hedging portfolio problem is viewed as a robust optimization problem. Tuning the parameter of the risk measure, we demonstrate by numerical examples that the two bounds approach to each other and converge to a price that is fair in the sense that seller and buyer face the same amount of risk.