This paper deals with the construction of “smooth good deals” (SGD), i.e., sequences of self-financing strategies whose global risk diverges to minus infinity and such that every security in every strategy of the sequence is a “smooth” derivative with a bounded delta. Since delta is bounded, digital options are excluded. In fact, the pay-off of every option in the sequence is continuos (and therefore jump-free) with respect to the underlying asset price. If the selected risk measure is the value at risk, then these sequences exist under quite weak conditions, since one can involve risks with both bounded and unbounded expectation, as well as non-friction-free pricing rules. Moreover, every strategy in the sequence is composed of a short European option plus a position in a riskless asset. If the chosen risk measure is a coherent one, then the general setting is more limited. Indeed, though frictions are still accepted, expectations and variances must remain finite. The existence of SGDs will be characterized, and computational issues will be properly addressed. It will be shown that SGDs often exist, and for the conditional value at risk, they are composed of the riskless asset plus easily replicable short European puts. The ideas presented may also apply in some actuarial problems such as the selection of an optimal reinsurance contract.

中文翻译：

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金融数学的黄金选择

本文涉及“顺畅交易”（SGD）的构建，即自筹资战略的序列，其整体风险分散到负无穷大，因此，该序列中每种策略中的每个证券都是“平稳”衍生产品，具有边界三角洲。由于增量是有界的，因此排除了数字期权。实际上，相对于基础资产价格，序列中每个选项的收益都是连续的（因此是无跳跃的）。如果选择的风险度量是风险价值，则这些序列存在的条件很弱，因为一个序列可能涉及具有无限制预期和无摩擦定价规则的风险。此外，序列中的每个策略都由空头欧洲期权加上无风险资产的头寸组成。如果选择的风险衡量是一致的，则一般设置会受到限制。确实，尽管仍然接受摩擦，但期望和方差必须保持有限。将对SGD的存在进行特征化，并适当解决计算问题。可以看出，SGD经常存在，并且对于处于风险中的有条件价值，它们由无风险资产加上易于复制的欧洲看跌期权构成。提出的想法也可能适用于一些精算问题，例如选择最佳再保险合同。它们由无风险资产加上易于复制的欧洲看跌期权组成。提出的想法也可能适用于一些精算问题，例如选择最佳再保险合同。它们由无风险资产加上易于复制的欧洲看跌期权组成。提出的想法也可能适用于一些精算问题，例如选择最佳再保险合同。