Optimal portfolios for the DC pension fund with mispricing under the HARA utility framework

<p style='text-indent:20px;'>This paper studies the optimal portfolio selection for defined contribution (DC) pension fund with mispricing. We adopt the general hyperbolic absolute risk averse (HARA) utility to describe the risk performance of the pension fund managers. The financial market comprises a risk-free asset, a pair of mispriced stocks, and the market index. Using the dynamic programming approach, we construct the Hamilton-Jacobi-Bellman (HJB) equation and obtain the explicit expressions for optimal portfolio choices with two methods. Finally, numerical analysis is presented to illustrate the sensitivity of the optimal portfolios to parameters of the financial market and contribution process. <b>200</b> words.</p>

An Optimal Compensation Agency Model for Sustainability under the Risk Aversion Utility Perspective

This paper explores how to construct a fair and optimal compensation system between the principal and the agent in the face of financial compensation agency problems during a limited period in relation to the concept of sustainability. In the construction of the principal’s compensation system, the agent’s degree of operational financial effort will affect the overall revenue function for reaching sustainability. Both the principal and the agent have a maximum expected utility in the negative exponential pattern of the general hyperbolic absolute risk aversion (HARA) utility function that satisfies their respective objective functions. The proposed model and numerical example analysis results prove that the compensation system for sustainability can provide a fair and optimal financial system, from a sustainability perspective. The main contribution of this study is the construction and development of an optimal compensation agency model for risk management, which is derived by considering the effect of risk aversion utility on revenue. The proposed model can provide a fair and feasible approach within the issue of compensation, from the viewpoint of sustainability, for an optimal compensation agency problem.

OPTIMAL DIVIDEND POLICY AND STOCK PRICES

We model a corporation dividend as an exchange option on stochastic cash flow and capital budge. Then we solve optimal dividend policy problem completely based on the dividend model under the assumption that the cash reservoir of a corporation follows a mean reverting process from empirical evidence and economic arguments. Our optimal dividend controls depend on explicitly with the cash flow and the capital budget of the corporation, and maximizes the HARA utility performance. We specify the unique optimal dividend control for the cash flow and the capital budge. Multiplicity or absence of optimal dividend policies are given. The stock price of the corporation is studied in terms of our stochastic dividend model. We find an explicit relation among the volatility of the stock price, the volatility of the cash flow and the volatility of the capital budget. The ex-dividend stock price is positively proportional to the stochastic cash flow and the probability of the dividend delta with respect to the cash flow, and negatively proportional to the capital budget and the probability of the dividend delta with respect to the capital budget. Hence, our approach provides another passage through which countercyclical volatility of the stock price can arise from the countercyclical cash flow and capital budget directly.

Do Time Preferences Matter in Intertemporal Consumption and Portfolio Decisions?

We study the intertemporal consumption and portfolio rules in the model with the general hyperbolic absolute risk aversion (HARA) utility. The equivalent approximation approach is employed to obtain the Hamilton-Jacobi-Bellman (HJB) equations, and a remarkable property is shown: portfolio rules are independent of the discount function. Moreover, both the consumption and portfolio rates are non-increasing functions of wealth. Particularly illustrative cases examined in detail are the models with the most adopted discount functions, including exponential discounting and hyperbolic discounting. Explicit solutions for intertemporal decisions are found for these special cases, revealing that individual’s time preferences affect the consumption rules only. Moreover, the time-consistent consumption rate under hyperbolic discounting is larger than its counterpart under exponential discounting.

Risk Aversion in a Dynamic Asset Allocation Experiment

We conduct a controlled laboratory experiment in the spirit of Merton (1971), in which subjects dynamically choose their portfolio allocation between a risk-free and risky asset. Using the optimal allocation of an investor with hyperbolic absolute risk aversion (HARA) utility, we fit the experimental choices to characterize the risk profile of our participants. Despite substantial heterogeneity, decreasing absolute risk aversion and increasing relative risk aversion are the predominant types. We also find some evidence of increased risk taking after a gain. Finally, the session level risk attitudes show a different profile than the individual descriptions of risk attitudes.