Dynamic Portfolio Choice under Time-Varying,Jumps,and Knight Uncertainty of Asset Return Process

By introducing a stochastic element to the double-jump diffusion framework to measure the Knight uncertainty of asset return process,the model of dynamic portfolio choice was built,which maximized the expected utility of terminal portfolio wealth.Through specifying the state function of uncertainty-aversion,it utilized the max-min method to derive the analytical solution of the model to study the effect of time-varying,jumps,and Knight uncertainty of asset return process on dynamic portfolio choice and their interactions.Results of comparative analysis show:the time-varying results in positive or negative intertemporal hedging demand of portfolio,which depends on the coefficient of investor's risk aversion and the correlation coefficient between return shift and volatility shift;the jumps in asset return overall reduce investor's demand for the risky asset,which can be enhanced or weakened by the jumps in volatility;due to the existing of Knight uncertainty,the investor avoids taking large position on risky asset,and improves portfolio's steady and immunity;the effects of the time-varying,jumps,and Knight uncertainty are interactive.

Dynamic Portfolio Choice under Uncertainty about Asset Return Model

The effect of uncertainty about stochastic diffusion model on dynamic portfolio choice of an investor who maximizes utility of terminal portfolio wealth was studied.It applied stochastic control method to obtain the closed-form solution of optimal dynamic portfolio,and used the Bayesian rule to estimate the model parameters to do an empirical study on two different samples of Shanghai Exchange Composite Index.Results show,model uncertainty results in positive or negative hedging demand of portfolio,which depends on investor's attitude toward risk;the effect of model uncertainty is more significant with the increasing of investment horizon,the decreasing of investor's risk-aversion degree,and the decreasing of information;predictability of risky asset return increases its allocation in portfolio,at the same time,the effect of model uncertainty also strengthens.

DYNAMIC PORTFOLIO CHOICE UNDER THE TIME-VARYING,JUMPS,AND KNIGHT UNCERTAINTY OF ASSET RETURN PROCESS

By introducing a stochastic element to the double-jump diffusion framework to measure the Knight uncertainty of asset return process, this paper builds the model of dynamic portfolio choice, which maximizes the expected utility of terminal portfolio wealth. Through specifying the state function of uncertainty-aversion, it utilizes the max-min method to derive the analytical solution of the model to study the effect of the time-varying, jumps, and Knight uncertainty of asset return process on dynamic portfolio choice and their interactions. Results of comparative analysis show： The time-varying results in positive or negative intertemporal hedging demand of portfolio, which depends on the coefficient of investor＇s risk aversion and the correlation coefficient between return shift and volatility shift; the jumps in asset return overall reduce investor＇s demand for the risky asset, which can be enhanced or weakened by the jumps in volatility; due to the existing of the Knight uncertainty, the investor avoids taking large position on risky asset, and the resulting is the improving of portfolio＇s steady and immunity. At last, an empirical study is done based on the samples of Shanghai Exchange Composite Index monthly return data from January 1997 to December 2009, which not only tests the theoretical analysis but also demonstrates that the proposed method in the paper is useful from the aspect of portfotio＇s equivalent utility.

Optimal Investment Strategy in Safe-region on Consumption and Portfolio Problem

This paper investigates an optimal investment strategy on consumption and portfolio problem, in which the investor must withdraw funds continuously at a given rate. By analyzing the evolving process of wealth, we give the definition of safe-region for investment. Moreover, in order to obtain the target wealth as quickly as possible, using Bellman dynamic programming principle, we get the optimal investment strategy and corresponding necessary expected time. At last we give some numerical computations for a set of different parameters.

Efficient online portfolio simulation using dynamic moving average model and benchmark index

Online portfolio selection and simulation are some of the most important problems in several research communities,including finance,engineering,statistics,artificial intelligence,machine learning,etc.The primary aim of online portfolio selection is to determine portfolio weights in every investment period(i.e.,daily,weekly,monthly,etc.)to maximize the investor’s final wealth after the end of investment period(e.g.,1 year or longer).In this paper,we present an efficient online portfolio selection strategy that makes use of market indices and benchmark indices to take advantage of the mean reversal phenomena at minimal risks.Based on empirical studies conducted on recent historical datasets for the period 2000 to 2015 on four different stock markets(i.e.,NYSE,S&P500,DJIA,and TSX),the proposed strategy has been shown to outperform both Anticor and OLMAR—the two most prominent portfolio selection strategies in contemporary literature.

Time Consistent Multi-period Worst-Case Risk Measure in Robust Portfolio Selection

In this paper,we first construct a time consistent multi-period worst-case risk measure,which measures the dynamic investment risk period-wise from a distributionally robust perspective.Under the usually adopted uncertainty set,we derive the explicit optimal investment strategy for the multi-period robust portfolio selection problem under the multi-period worst-case risk measure.Empirical results demonstrate that the portfolio selection model under the proposed risk measure is a good complement to existing multi-period robust portfolio selection models using the adjustable robust approach.