Dynamic utility-based good deal bounds
Dynamic utility-based good deal bounds
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基于动态效用的优惠界限
DOI：
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发表时间：
2007
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通讯作者：
Fam ETH
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文献类型：
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作者：
M. Schweizer;T. Wien;Versicherungsmathematik Departement;Fam ETH
我们引入并研究了基于期望效用的非好交易估值界。基于效用的好交易是指其预期效用与其价格的效用相比太高的支付。禁止好的交易通过二元性导致对定价核心的限制，从而给支付的估值带来了比单纯没有套利更严格的估值界限。我们的方法在几个方向上推广了·Cernä(2003)的早期工作：我们给出了一般概率空间的严格结果，而不是Flinite>；我们系统地利用对偶结果提供了一个具有简单论证的简化方法；我们对静态和动态情况严格地做了所有这些；我们给出了时间动态设置下局部和全局(条件)定价核限制的系统比较。对于动态情况，我们在Levy框架中表明，通过对非好交易估值措施的瞬时市场风险价格施加局部条件限制，可以给出具有非常好的动态性质的估值界限，作为随时间推移的过程。我们还表明，总体上，全球限制不能产生这样的结果。
We introduce and study no-good-deal valuation bounds deflned in terms of ex- pected utility. A utility-based good deal is a payofi whose expected utility is too high in comparison to the utility of its price. Forbidding good deals induces, via duality, restrictions on pricing kernels and thereby gives tighter valuation bounds on payofis than absence of arbitrage alone. Our approach extends earlier work by • Cern¶ (2003) in several directions: We give rigorous results for a general proba- bility space instead of flnite ›; we systematically use duality results to provide a streamlined approach with simple arguments; we do all this rigorously for both static and dynamic situations; and we give a systematic comparison between local and global (conditional) pricing kernel restrictions for the temporally dynamic setting. For the dynamic case, we show in a Levy framework that deflning no- good-deal valuation measures by imposing local conditional restrictions on their instantaneous market prices of risk gives valuation bounds having very good dy- namic properties as processes over time. We also show that global restrictions cannot yield such results in general.