The question of optimal portfolio is that finds the trading strategy satisfying the maximal expected utility function subject to some constraints. There is the optimal trading strategy under the risk neutral probabili...The question of optimal portfolio is that finds the trading strategy satisfying the maximal expected utility function subject to some constraints. There is the optimal trading strategy under the risk neutral probability measure （martingale measure） if and only if there is no-arbitrage opportunity in the market. This paper argues the optimal wealth and the optimal value of expected utility with different utility function.展开更多
It is studied that the stochastic control problem of maxi-mizing expected utility from terminal wealth and/or con-sumption,when the portfolio is constrained to take val-ues in a given closed,convex subset of R,and in ...It is studied that the stochastic control problem of maxi-mizing expected utility from terminal wealth and/or con-sumption,when the portfolio is constrained to take val-ues in a given closed,convex subset of R,and in the pr-esence of a higher interest rate for borrowing.The set-ting is that of a continuous-time,Ito process model for the underlying asset prices.The existence of portfolio op-timization under constraints and with higher interest ratefor borrowing than for lending is discussed,and the so-lution for logarithmic utility function is presented.展开更多
We study mean-field type optimal stochastic control problem for systems governed by mean-field controlled forward-backward stochastic differential equations with jump processes,in which the coefficients depend on the ...We study mean-field type optimal stochastic control problem for systems governed by mean-field controlled forward-backward stochastic differential equations with jump processes,in which the coefficients depend on the marginal law of the state process through its expected value.The control variable is allowed to enter both diffusion and jump coefficients.Moreover,the cost functional is also of mean-field type.Necessary conditions for optimal control for these systems in the form of maximum principle are established by means of convex perturbation techniques.As an application,time-inconsistent mean-variance portfolio selectionmixed with a recursive utility functional optimization problem is discussed to illustrate the theoretical results.展开更多
文摘The question of optimal portfolio is that finds the trading strategy satisfying the maximal expected utility function subject to some constraints. There is the optimal trading strategy under the risk neutral probability measure （martingale measure） if and only if there is no-arbitrage opportunity in the market. This paper argues the optimal wealth and the optimal value of expected utility with different utility function.
文摘It is studied that the stochastic control problem of maxi-mizing expected utility from terminal wealth and/or con-sumption,when the portfolio is constrained to take val-ues in a given closed,convex subset of R,and in the pr-esence of a higher interest rate for borrowing.The set-ting is that of a continuous-time,Ito process model for the underlying asset prices.The existence of portfolio op-timization under constraints and with higher interest ratefor borrowing than for lending is discussed,and the so-lution for logarithmic utility function is presented.
基金The first author was partially supported by Algerian CNEPRU Project Grant B01420130137,2014-2016.
文摘We study mean-field type optimal stochastic control problem for systems governed by mean-field controlled forward-backward stochastic differential equations with jump processes,in which the coefficients depend on the marginal law of the state process through its expected value.The control variable is allowed to enter both diffusion and jump coefficients.Moreover,the cost functional is also of mean-field type.Necessary conditions for optimal control for these systems in the form of maximum principle are established by means of convex perturbation techniques.As an application,time-inconsistent mean-variance portfolio selectionmixed with a recursive utility functional optimization problem is discussed to illustrate the theoretical results.
