This paper considers a consumption and investment decision problem with a higher interest rate for borrowing as well as the dividend rate.Wealth is divided into a riskless asset and risky asset with logrithmic Brownia...This paper considers a consumption and investment decision problem with a higher interest rate for borrowing as well as the dividend rate.Wealth is divided into a riskless asset and risky asset with logrithmic Brownian motion price fluctuations.The stochastic control problem of maximizating expected utility from terminal wealth and consumption is studied.Equivalent conditions for optimality are obtained.By using duality methods,the existence of optimal portfolio consumption is proved,and the explicit solutions leading to feedback formulae are derived for deteministic coefficients.展开更多
Certain Merton type consumption−investment problems under partial information are reduced to the ones of full information and within the framework of a complete market model.Then,specializing to conditionally log−Gaus...Certain Merton type consumption−investment problems under partial information are reduced to the ones of full information and within the framework of a complete market model.Then,specializing to conditionally log−Gaussian diffusion models,concrete analysis about the optimal values and optimal strategies is performed by using analytical tools like Feynman−Kac formula,or HJB equations.The explicit solutions to the related forward-backward equations are also given.展开更多
In this work, for a control consumption-investment process with the discounted reward optimization criteria, a numerical estimate of the stability index is made. Using explicit formulas for the optimal stationary poli...In this work, for a control consumption-investment process with the discounted reward optimization criteria, a numerical estimate of the stability index is made. Using explicit formulas for the optimal stationary policies and for the value functions, the stability index is explicitly calculated and through statistical techniques its asymptotic behavior is investigated (using numerical experiments) when the discount coefficient approaches 1. The results obtained define the conditions under which an approximate optimal stationary policy can be used to control the original process.展开更多
文摘This paper considers a consumption and investment decision problem with a higher interest rate for borrowing as well as the dividend rate.Wealth is divided into a riskless asset and risky asset with logrithmic Brownian motion price fluctuations.The stochastic control problem of maximizating expected utility from terminal wealth and consumption is studied.Equivalent conditions for optimality are obtained.By using duality methods,the existence of optimal portfolio consumption is proved,and the explicit solutions leading to feedback formulae are derived for deteministic coefficients.
文摘Certain Merton type consumption−investment problems under partial information are reduced to the ones of full information and within the framework of a complete market model.Then,specializing to conditionally log−Gaussian diffusion models,concrete analysis about the optimal values and optimal strategies is performed by using analytical tools like Feynman−Kac formula,or HJB equations.The explicit solutions to the related forward-backward equations are also given.
文摘In this work, for a control consumption-investment process with the discounted reward optimization criteria, a numerical estimate of the stability index is made. Using explicit formulas for the optimal stationary policies and for the value functions, the stability index is explicitly calculated and through statistical techniques its asymptotic behavior is investigated (using numerical experiments) when the discount coefficient approaches 1. The results obtained define the conditions under which an approximate optimal stationary policy can be used to control the original process.
