Using expectations regarding utilities to make decisions in a risk environment hides a paradox,which is called the expected utility enigma.Moreover,the mystery has not been solved yet;an imagined utility function on t...Using expectations regarding utilities to make decisions in a risk environment hides a paradox,which is called the expected utility enigma.Moreover,the mystery has not been solved yet;an imagined utility function on the risk-return plane has been applied to establish the mean-variance model,but this hypothetical utility function not only lacks foundation,it also holds an internal contradiction.This paper studies these basic problems.Through risk preference VNM condition is proposed to solve the expected utility enigma.How can a utility function satisfy the VNM condition?This is a basic problem that is hard to deal with.Fortunately,it is found in this paper that the VNM utility function can have some concrete forms when individuals have constant relative risk aversion.Furthermore,in order to explore the basis of mean-variance utility,an MV function is founded that is based on the VNM utility function and rooted in underlying investment activities.It is shown that the MV function is just the investor's utility function on the risk-return plane and that it has normal properties.Finally,the MV function is used to analyze the laws of investment activities in a systematic risk environment.In doing so,a tool,TRR,is used to measure risk aversion tendencies and to weigh risk and return.展开更多
We introduce and analyze a class of forward performance criteria in incomplete markets in the presence of model ambiguity.Incompleteness stems from general investment constraints,while model uncertainty is represented...We introduce and analyze a class of forward performance criteria in incomplete markets in the presence of model ambiguity.Incompleteness stems from general investment constraints,while model uncertainty is represented by a convex and compact set of plausible model parameter processes.Following the max-min criteria in traditional(backward)robust control,we formulate similar criteria for the robust forward performance processes and focus on the rich class of time-monotone processes.We provide a novel PDE characterization and a semi-explicit saddle-point construction of the robust forward performance criteria and their optimal policies.Furthermore,we present additional results within the class of homothetic constant relative risk aversion(CRRA)processes.Within this class,we investigate the relationship between forward performance processes on wealth and those on consumption,establishing an interesting dominance through time.展开更多
文摘Using expectations regarding utilities to make decisions in a risk environment hides a paradox,which is called the expected utility enigma.Moreover,the mystery has not been solved yet;an imagined utility function on the risk-return plane has been applied to establish the mean-variance model,but this hypothetical utility function not only lacks foundation,it also holds an internal contradiction.This paper studies these basic problems.Through risk preference VNM condition is proposed to solve the expected utility enigma.How can a utility function satisfy the VNM condition?This is a basic problem that is hard to deal with.Fortunately,it is found in this paper that the VNM utility function can have some concrete forms when individuals have constant relative risk aversion.Furthermore,in order to explore the basis of mean-variance utility,an MV function is founded that is based on the VNM utility function and rooted in underlying investment activities.It is shown that the MV function is just the investor's utility function on the risk-return plane and that it has normal properties.Finally,the MV function is used to analyze the laws of investment activities in a systematic risk environment.In doing so,a tool,TRR,is used to measure risk aversion tendencies and to weigh risk and return.
文摘We introduce and analyze a class of forward performance criteria in incomplete markets in the presence of model ambiguity.Incompleteness stems from general investment constraints,while model uncertainty is represented by a convex and compact set of plausible model parameter processes.Following the max-min criteria in traditional(backward)robust control,we formulate similar criteria for the robust forward performance processes and focus on the rich class of time-monotone processes.We provide a novel PDE characterization and a semi-explicit saddle-point construction of the robust forward performance criteria and their optimal policies.Furthermore,we present additional results within the class of homothetic constant relative risk aversion(CRRA)processes.Within this class,we investigate the relationship between forward performance processes on wealth and those on consumption,establishing an interesting dominance through time.
