A Study On The Problem Of Dynamic Portfolio Choice Under Continuous-time

Portfolio choice, especially dynamic portfolio choice, is among the most important problems in financial economics and asset pricing in particular, and is the cornerstone of financial economics. Comparing with the static portfolio choice, dynamic portfolio choice embodies dynamic behavior of asset price, reflects the characteristic of security market, and describes the process of investment decision; provides an intertemporal optimal method of how allocates the limited source for economical individual to realize his or her investment object under uncertain environment; and is to some extent helpful to realize the rational expected equilibrium of security market, and make it function. So study on the problem of dynamic portfolio choice has importtant theoretical and practical meaning.Comparing with dynamic portfolio choice under discrete-time, dynamic portfolio choice under continuous-time has advantages on obtaining the analytical solution of optimal portfolio choice, deeply analyzing and explaining the problems. Based on these reasons, this thesis uses continuous-time equity return model to describe the dynamic characteristic of risky asset price, and studies the relations between dynamic portfolio choice and time-varying or predictability of investment opportunity set, jumps during the process of asset price, parametric uncertainty of investment opportunity set, and uncertainty of continuous-time equity return model; applies the method of stochastic control to obtain the optimal closed-form solution or analytical expression of dynamic portfolio choice, which maximizes the expected power utility of investor's terminal wealth, and does theoretical analysis; with the help of computer, uses the continuous compounding monthly returns of Shanghai Exchange Composite Index as study sample, and applies the Bayesian analysis framework to obtain future parameter distribution and spectral generalized method of moments to estimate parameter in the model to do empirical study in order to support and deepen the theoretical analysis; at last, gives the related conclusion that can provide some evidence for investment practice, and explains some abnormal phenomena in security market.At first, in general set, assuming that asset return follows Ito's diffusion process, it studies the relation between time-varying of investment opportunity set and dynamic portfolio choice. Theoretical analysis shows, investment opportunity set is time-varying or not and investor's different preferences result in two behaviors of dynamic portfolio choice: dynamic myopic behavior and dynamic optimal behavior; dynamic myopic behavior is similar to static portfolio choice, and satisfies the Two-Fund Theory, dynamic optimal behavior embodies investor's intertemporal hedging demands for portfolio, and satisfies the generalized Three-Fund Theory; during the process of dynamic portfolio decision, the long-term investor, who faces time-varying investment opportunity set, cares about unfavorable shocks to investment opportunity—the productivity of wealth—as well as risk of wealth itself, so they may wish to hedge their exposures to wealth productivity shocks, and give rise to intertemporal hedging demands for financial risky asset.Then, assuming that asset return follows Ito's diffusion process, it studies the relation between the uncertainty about expected return and variance of risky asset and dynamic portfolio choice by introducing parametric uncertainty into the model. Theoretical and empirical analysis show, parametric uncertainty results in investor's hedging demands for portfolio; the hedging demands is negative(positive) when investor's risk aversion is more(less) than that of logarithmic utility; the effects of parametric uncertainty will weaken with the shortening of horizon, the increasing of information and investor's risk aversion; the effect of expected return's uncertainty is stronger than that of variance's uncertainty; the effect of parametric uncertainty under one order autoregressive process is stronger than that of parametric uncertainty under iid. normal process; the puzzle of risk premium can be explained by dynamic portfolio choice.And then, assuming that asset return follows jump-diffusion process, it studies the relation between the predictability and jumps during return's process and dynamic portfolio choice, mainly explains the relation and builds the linkage between predictability and jumps from the aspect of moment analysis, and then expands to the double-jump diffusion process. Theoretical and empirical analysis show, positive (negative) skewness of return's distribution results in the increasing of risky asset investment, excess kurtosis of return's distribution results in the decreasing of risky asset investment, and their effect will strengthen with the increasing of investor's risk aversion; although the time-varying of expected return increases the conditional variance of asset return, predictability results in investor's hedging demands for portfolio, positive or negative hedging demands depends on investor's risk aversion and relative coefficient between the volatility of asset return and that of expected return, the quantity of hedging demands will decrease with the shortening of horizon; on the whole, jumps result in the decreasing of risky asset investment, but positive (negative) jump will weaken (strengthen) this trend; jumps of variance don't affect myopic demands of portfolio choice, but affects the jump hedging demands of return process, the effect depends on the direction of variance's jump and investor's risk aversion; jumps to some extent can enhance the portfolio's stability due to the predictability.At last, introducing a new stochastic variable into stochastic volatility model to measure uncertain difference due to model uncertainty, it studies the relation between time-varying expected return and variance, predictability, uncertainty-aversion and dynamic portfolio choice. Theoretical and empirical analysis show, predictability results in investor's hedging demands for portfolio, positive or negative hedging demands depends on investor's risk aversion and relative coefficient between the volatility of asset return and that of variance, the quantity of hedging demands will increase with the increasing of horizon; whether the original position of risky asset is long or short, uncertainty-aversion will decrease the position, and enhances portfolio immunity; the stability of portfolio increases due to the cushioning effect of predictability and uncertainty-aversion within horizon; dynamic portfolio choice can explain the puzzle of non-market participation, but is failure to explain the phenomena of non-market participation in Shanghai security market.The innovations of this thesis are as follows:①During the process of dynamic portfolio choice under continuous-time, it considers that expected return and variance are all uncertain, and does a comparative study for different return process. This not only upgrades study's practical implication, but also makes up the shortage of current study.②From the aspect of moment analysis, it clearly demonstrate the relation between portfolio choice and the first four moments of asset return, explains the characteristic of dynamic portfolio choice, and builds the linkage between predictability and jumps.③By specifying state function of uncertainty-aversion, it applies the theory of penal function to study dynamic portfolio choice under model uncertainty through the utility cost of wealth. This makes up the shortage of current study.