Duplicating and pricing contingent claims with constrained portfolios  

作　　者：彭实戈 杨峰 

机构地区：[1]Institute of Mathematics and System Science, Shandong University, Jinan 250100, China

出　　处：《Progress in Natural Science:Materials International》1998年第6期11-20,共10页自然科学进展·国际材料（英文版）

基　　金：Project partially supported by the National Natural Science Foudation of China (Grant No. 79790130)

摘　　要：The problem of pricing contingent claims is studied in the situation where the constrains imposed on an investor’s portfolios cannot be neglected. The following results are obtained: ( i ) under elastic rules, the cost to duplicate a contingent claim exists and is unique; ( ii ) this cost depends nonlinearly and convexly on the contingent claim; ( iii ) the cost under rigid rules is the limit of the corresponding elastic rules when passing the penalty to infint ty. This cost is also a nonlinear and convex functional of the contingent claim Due to nonlineanty, the cost of duplication may or may not be the non-arbitrage price of the contingent claim. It depends on how the market organizes the production of contingent claims. The conclusion that the cost of duplication is a convex functional of the contingent claim provides an explanation why securitiezed financial services are often high profitable business.The problem of pricing contingent claims is studied in the situation where the constrains imposed on an investor’s portfolios cannot be neglected. The following results are obtained: ( i ) under elastic rules, the cost to duplicate a contingent claim exists and is unique; ( ii ) this cost depends nonlinearly and convexly on the contingent claim; ( iii ) the cost under rigid rules is the limit of the corresponding elastic rules when passing the penalty to infint ty. This cost is also a nonlinear and convex functional of the contingent claim Due to nonlineanty, the cost of duplication may or may not be the non-arbitrage price of the contingent claim. It depends on how the market organizes the production of contingent claims. The conclusion that the cost of duplication is a convex functional of the contingent claim provides an explanation why securitiezed financial services are often high profitable business.

关 键 词：CONTINGENT CLAIM elastic RULES RIGID RULES BACKWARD stochastic differential equations. 

分 类 号：N[自然科学总论]