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
Owing to the fact that the major challenge of predicting the risk of having bipolar is the absence of a gold standard to distinguish between true cases and false positive;this study employed the extension of cubic spl...Owing to the fact that the major challenge of predicting the risk of having bipolar is the absence of a gold standard to distinguish between true cases and false positive;this study employed the extension of cubic spline function to the multinomial model to explore the risk tendency of unnoticed early bipolar across three different groups of mood disorder. The intermediate group was used to accommodate for false negative and false positive while mapping the true value of bipolar risk tendency across the three groups to a scale. Hence for all distributions of “yes” ticked in a mood disorder questionnaire, the study predicts the bipolar risk tendency while simultaneously accommodating for the patients response bias. The coefficients of the polynomial are obtained using the maximum likelihood method. The spline graph reveals how bipolar disorder build up slowly and lingers in the body for long without been noticed due to fluctuations in risk tendency of the mood scores.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Owing to the fact that the major challenge of predicting the risk of having bipolar is the absence of a gold standard to distinguish between true cases and false positive;this study employed the extension of cubic spline function to the multinomial model to explore the risk tendency of unnoticed early bipolar across three different groups of mood disorder. The intermediate group was used to accommodate for false negative and false positive while mapping the true value of bipolar risk tendency across the three groups to a scale. Hence for all distributions of “yes” ticked in a mood disorder questionnaire, the study predicts the bipolar risk tendency while simultaneously accommodating for the patients response bias. The coefficients of the polynomial are obtained using the maximum likelihood method. The spline graph reveals how bipolar disorder build up slowly and lingers in the body for long without been noticed due to fluctuations in risk tendency of the mood scores.
