论文标题
通过TSALLIS相对熵在不完整的市场中定价原理
Pricing principle via Tsallis relative entropy in incomplete market
论文作者
论文摘要
在不完整的布朗运动市场环境中，引入了针对无法获得的$ Q $ thend界有限的特定主张的定价原则。买方评估了根据``扭曲的ra脚衍生物'''的偶然性主张，并通过tsallis相对熵对等效的玛格尔措施进行调整。事实证明，定价原则是一致且无套利的定价规则。更重要的是，发现该定价原理与发电机$ f（y）| z |^2 $类型的向后随机微分方程密切相关。定价功能与可达到的索赔的价格兼容。除了翻译不变性外，定价原理过程还有许多优雅的特性，例如单调性和凹度等。定价功能在最小的martingale量度定价与有条件的确定性之间显示在$ q $ uppertential实用程序下。还研究了定价原理对歧义厌恶系数的渐近行为。
A pricing principle is introduced for non-attainable $q$-exponential bounded contingent claims in an incomplete Brownian motion market setting. The buyer evaluates the contingent claim under the ``distorted Radon-Nikodym derivative'' and adjustment by Tsallis relative entropy over a family of equivalent martingale measures. The pricing principle is proved to be a time consistent and arbitrage-free pricing rule. More importantly, this pricing principle is found to be closely related to backward stochastic differential equations with generators $f(y)|z|^2$ type. The pricing functional is compatible with prices for attainable claims. Except translation invariance, the pricing principle processes lots of elegant properties such as monotonicity and concavity etc. The pricing functional is showed between minimal martingale measure pricing and conditional certainty equivalent pricing under $q$-exponential utility. The asymptotic behavior of the pricing principle for ambiguity aversion coefficient is also investigated.
