On the super replication price of unbounded claims

被引:13
作者
Biagini, S
Frittelli, M
机构
[1] Univ Perugia, Dipartimento Econ, Sez Finanza Matemat, I-06123 Perugia, Italy
[2] Univ Florence, Dipartimento Matemat Decis, I-50134 Florence, Italy
关键词
super replication price; generalized entropy; reasonable asymptotic elasticity; preferences; incomplete markets; utility maximization; duality;
D O I
10.1214/105051604000000459
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
In an incomplete market the price of a claim f in general cannot be uniquely identified by no arbitrage arguments. However, the "classical" super replication price is a sensible indicator of the (maximum selling) value of the claim. When f satisfies certain pointwise conditions (e.g., f is bounded from below), the super replication price is equal to sup(Q) E-Q[f], where Q varies on the whole set of pricing measures. Unfortunately, this price is often too high: a typical situation is here discussed in the examples. We thus define the less expensive weak super replication price and we relax the requirements on f by asking just for "enough" integrability conditions. By building up a proper duality theory, we show its economic meaning and its relation with the investor's preferences. Indeed, it turns out that the weak super replication price of f coincides with sup(Qis an element ofMphi) E-Q[f], where M-phi, is the class of pricing measures with finite generalized entropy (i.e., E[phi(dQ/dP)] < infinity) and where phi is the convex conjugate of the utility function of the investor.
引用
收藏
页码:1970 / 1991
页数:22
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