风险中性概率下的凸优化
Convex Optimization Over Risk-Neutral Probabilities
摘要：
我们考虑一组衍生品，这些衍生品的价格取决于标的资产在到期日或到期日的价格。不存在套利等价于价格存在风险中性概率分布;特别是，任何风险中性分布都可以被解释为证明不存在套利。我们感兴趣的情况下，有多个风险中性概率。我们描述了一些风险中性价格概率凸集上的凸优化问题。这些包括计算风险中性概率集上的累积分布、VaR、CVaR和其他量的界限。在对标的价格离散化后，这些问题就变成了有限维的凸或拟凸优化问题，因此是容易处理的。我们使用标准普尔500指数和比特币的实物期权和期货定价数据来说明我们的方法。
英文摘要：
We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in particular, any risk neutral distribution can be interpreted as a certificate establishing that no arbitrage exists. We are interested in the case when there are multiple risk-neutral probabilities. We describe a number of convex optimization problems over the convex set of risk neutral price probabilities. These include computation of bounds on the cumulative distribution, VaR, CVaR, and other quantities, over the set of risk-neutral probabilities. After discretizing the underlying price, these problems become finite dimensional convex or quasiconvex optimization problems, and therefore are tractable. We illustrate our approach using real options and futures pricing data for the S&P 500 index and Bitcoin.
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