A stochastic control model of investment, production and consumption
Wendell H. Fleming,Tao Pang +1 more
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In this article, the authors consider a stochastic control model in which an economic unit has productive capital and also liabilities in the form of debt, and choose investment and consumption controls which maximize total expected discounted HARA utility of consumption.Abstract:
We consider a stochastic control model in which an economic unit has productive capital and also liabilities in the form of debt. The worth of capital changes over time through investment as well as through random Brownian fluctuations in the unit price of capital. Income from production is also subject to random Brownian fluctuations. The goal is to choose investment and consumption controls which maximize total expected discounted HARA utility of consumption. Optimal control policies are found using the method of dynamic programming. In case of logarithmic utility, these policies have explicit forms.read more
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References
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Book
Controlled Markov processes and viscosity solutions
Wendell H. Fleming,H. Mete Soner +1 more
TL;DR: In this paper, an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions is given, as well as a concise introduction to two-controller, zero-sum differential games.
Book
Deterministic and stochastic optimal control
TL;DR: In this paper, the authors considered the problem of optimal control of Markov diffusion processes in the context of calculus of variations, and proposed a solution to the problem by using the Euler Equation Extremals.
Book
Derivatives in Financial Markets with Stochastic Volatility
TL;DR: The Black-Scholes theory of derivative pricing has been applied to derivatives as discussed by the authors, where the rate of mean-reverting stochastic volatility has been estimated for European derivatives.
Journal ArticleDOI
A solution approach to valuation with unhedgeable risks
TL;DR: A class of stochastic optimization models of expected utility in markets with stochastically changing investment opportunities is studied, which expresses the value function in terms of the solution of a linear parabolic equation, with the power exponent depending only on the coefficients of correlation and risk aversion.
Journal ArticleDOI
Risk-Sensitive Dynamic Asset Management
TL;DR: In this article, the authors developed a continuous time portfolio optimization model where the mean returns of individual securities or asset categories are explicitly affected by underlying economic factors such as dividend yields, a firm's return on equity, interest rates, and unemployment rates.