Optimal portfolio in discrete-time under HARA utility function

Abstract

In this study we are going to discuss about optimal dynamic portfolio strategy given the new information of the market to the investor. The objective is to find the optimal strategy that maximizes the expected total hyperbolic absolute risk aversion (HARA)-utility of investor weight portfolio over finite life time. There are two assets that take place in to the dynamic portfolio model, risky asset and risk-free bond with constant interest rate. The underlying stock price is obtained under binomial process of Markov chain approximation of diffusion process. The stochastic dynamic programming is used as the approach to solve the problem. In contrast to the continuoustime counterpart, the optimal trading strategies are found to be time-dependent in recursive manners. Sufficient conditions for short selling are given in terms of physical and martingale probabilities of the stock price.

Optimal Portfolio Analysis of Listed Companies in IDX 30

“…There are two mathematical models to describe the portfolio process, namely static and dynamic portfolio models. A static portfolio is a replicated portfolio for a given static asset while a dynamic portfolio is a replicated portfolio for a given asset, this is for small changes in the underlying parameters, such as time, asset prices that vary and always adjust to the portfolio itself [9].…”

“…The Mean Variance Model means that for a given expected return, the variance of the return will reach the lowest value assuming that the investor's choice of portfolio will depend on the mean and variance. After determining an acceptable level of risk by quantifying risk using variance, an investor may seek the highest return while determining risk using variance [9]. Markowitz [3] developed a mean-variance model using stock diversification, where several types of assets are formed and combined in a portfolio.…”