The General Merton Problem Of An Ambiguity-averse Investor

Based on the complexity of global economic dynamics,people often cannot accurately identify the evolution of risk factors.Financial modeling is inevitably subject to the ambi-guity of the model.This paper establishes a portfolio model with consumption by using the constant absolute risk aversion utility function(CARA)and multiple proiors expected utility in the ambiguity framework to solve the problem of investors5 uncertainty about mean return and volatility estimates.Firstly,under the ambiguity framework,using the CARA utility function,a one-dimensional portfolio model with consumption is established.Assuming that the average yield and volatility of stock prices have ambiguity uncertainty,investors are risk aversion and am-biguity aversion,using the minimum and minimum expected utility to establish the problem of stochastic optimal control and Hamilton-Jacobi-Bellmann-Isac(HJBI)partial differential equation.Given the allowable volatility process,consider the average yield of stocks to sat-isfy a certain ambiguous interval,and solve the optimal portfolio and consumption through HJBI equation,and give the analytical formula of the optimal wealth process.Secondly,analogously,in this paper,a multidimensional model is established by using a research method similar to the one-dimensional model.When the stock volatility has am-biguity uncertainty and the return rate has ellipsoid uncertainty depending on the volatility,the stochastic optimal control problem is also given.Corresponding HJBI equations,and the most pessimistic probability measure of investors are given by solving partial differential equations.By constructing a binary function,this paper gives an analytical solution of the optimal wealth process.Finally,selecting one risk asset in one-dimensional for case analysis and more than one risk assets are selected in multi-dimensional for case analysis.By collecting and calculating the data during the sample period,the optimal investment strategies for the external prediction period are obtained.