Bosco Yu

Objective comparisons of the optimal portfolios corresponding to different utility functions

This paper considers the effects of some frequently used utility functions in portfolio selection by comparing the optimal investment outcomes corresponding to these utility functions. Assets are assumed to form a complete market of the Black-Scholes type. Under consideration are four frequently used utility functions: the power, logarithm, exponential and quadratic utility functions. To make objective comparisons, the optimal terminal wealths are derived by integration representation. The optimal strategies which yield optimal values are obtained by the integration representation of a Brownian martingale. The explicit strategy for the quadratic utility function is new. The strategies for other utility functions such as the power and the logarithm utility functions obtained this way coincide with known results obtained from Mertons dynamic programming approach.

A simulation-based approach to the study of coefficient of variation of dividend yields

Existing empirical studies of dividend yields and dividend policies either make no assumption or the normal distribution of the dividend yields data. The statistical results will be biased because they cannot reflect the finite support set property of dividend yields which can only range from 0 to 1. We posit that the assumption that dividend yields follow a beta distribution is more appropriate. The coefficient of variation (CV) is used to measure the stability of dividend yields. If we assume dividend yields follow a normal distribution, then the maximum likelihood estimate for coefficient of variation is given by . This only gives us a point estimate, which cannot depict the full picture of the sampling distribution of the coefficient of variation. A simulation-based approach is adopted to estimate CV under the beta distribution. This approach will give us a point estimate as well as the empirical sampling distribution of CV. With this approach, we study the stability of dividend yields of the Hang Seng index and its sub-indexes of the Hong Kong stock market and compare the results with the traditional approach.

A simulation based approach to the parameter estimation for the three-parameter gamma distribution☆

Abstract The gamma distribution is one of the commonly used statistical distribution in reliability. While maximum likelihood has traditionally been the main method for estimation of gamma parameters, Hirose has proposed a continuation method to parameter estimation for the three-parameter gamma distribution. In this paper, we propose to apply Markov chain Monte Carlo techniques to carry out a Bayesian estimation procedure using Hirose’s simulated data as well as two real data sets. The method is indeed flexible and inference for any quantity of interest is readily available.