Predictable forward performance processes in complete markets  

作　　者：Bahman Angoshtari 

机构地区：[1]Department of Mathematics,University of Miami,Coral Gables,FL 33146,USA

出　　处：《Probability, Uncertainty and Quantitative Risk》2023年第2期141-176,共36页概率、不确定性与定量风险（英文）

基　　金：supported by the National Science Foundation(Grant No.DMS-1929348).

摘　　要：We establish existence of Predictable Forward Performance Processes(PFPPs)in conditionally complete markets,which has been previously shown only in the binomial setting.Our market model can be a discrete-time or a continuous-time model,and the investment horizon can be finite or infinite.We show that the main step in construction of PFPPs is solving a one-period problem involving an integral equation,which is the counterpart of the functional equation found in the binomial case.Although this integral equation has been partially studied in the existing literature,we provide a new solution method using the Fourier transform for tempered distributions.We also provide closedform solutions for PFPPs with inverse marginal functions that are completely monotonic and establish uniqueness of PFPPs within this class.We apply our results to two special cases.The first one is the binomial market and is included to relate our work to the existing literature.The second example considers a generalized Black–Scholes model which,to the best of our knowledge,is a new result.

关 键 词：Forward performance processes Predictable preference Complete market Integral equation Completely monotonic inverse marginal Deconvolution Fourier transform 

分 类 号：O21[理学—概率论与数理统计]