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The optimal investment consumption problem for a single riskless bond, a zero-coupon bond and a risky stock modeled by the CIR interest process has been established. The investment objective is maximizing the utility of his consumption and terminal wealth. By the stochastic dynamic programming principle, the HJB equation for the optimal solution is given. In the case of constant relative risk aversion...
The optimal portfolio problem for a riskless asset and (n+1) risky stocks is developed. The stochastic short-term interest rate with Vasicek dynamics affects the prices of the stocks. The investment objective is maximizing expected CRRA utility of the difference between the terminal wealth and the stochastic benchmark with the constraint: the terminal wealth is more than the stochastic benchmark....
Portfolio stochastic control problem is proposed and analyzed for a market consisting of one bank account and multiple stocks. The market parameters, including the bank interest rate and the appreciation and volatility rates of the stocks, depend on the market mode that switches among a finite number of states. The random regime switching is assumed to be independent of the underlying Brownian motion...
Suppose that a market consists of a foreign exchange deposit and a risky stock, the optimal portfolio problem with consumption is formulated under the continuous-time mean- variance frame. By using the stochastic linear-square control theory, the explicit optimal trading strategies and the closed-form efficient frontier are derived. The numerical example shows that with the increase of the consumption...
The optimal portfolio problem for a single riskless bond and risky stock modeled by jump-diffusion process has been established. The investment objective is maximizing the utility of his consumption and terminal wealth. The problem is formulated as a stochastic optimal control problem. The verification theorem and HJB equation for the optimal trading strategies are given by stochastic optimal control...
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