Optimum consumption and portfolio rules in a continuous-time model☆
TLDR
In this paper, the authors considered the continuous-time consumption-portfolio problem for an individual whose income is generated by capital gains on investments in assets with prices assumed to satisfy the geometric Brownian motion hypothesis, which implies that asset prices are stationary and lognormally distributed.About:
This article is published in Journal of Economic Theory.The article was published on 1971-12-01 and is currently open access. It has received 4952 citations till now. The article focuses on the topics: Geometric Brownian motion & Intertemporal portfolio choice.read more
Citations
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Martingales and stochastic integrals in the theory of continuous trading
TL;DR: In this paper, a general stochastic model of a frictionless security market with continuous trading is developed, where the vector price process is given by a semimartingale of a certain class, and the general Stochastic integral is used to represent capital gains.
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An intertemporal asset pricing model with stochastic consumption and investment opportunities
TL;DR: In this paper, the authors derived a single-beta asset pricing model in a multi-good, continuous-time model with uncertain consumption-goods prices and uncertain investment opportunities.
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Evaluating Natural Resource Investments
TL;DR: In this article, it is shown that continuous time arbitrage and stochastic control theory may be used not only to value such projects but also to determine the optimal policies for developing, managing, and abandoning them.
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Backward Stochastic Differential Equations in Finance
TL;DR: In this article, different properties of backward stochastic differential equations and their applications to finance are discussed. But the main focus of this paper is on the theory of contingent claim valuation, especially cases with constraints.
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On estimating the expected return on the market: An exploratory investigation
TL;DR: In this article, three models of equilibrium expected market returns which reflect the dependence of the market return on the interest rate were analyzed and the non-negativity restriction of the expected excess return was explicity included as part of the specification.
References
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Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case
TL;DR: In this paper, the combined problem of optimal portfolio selection and consumption rules for an individual in a continuous-time model was examined, where his income is generated by returns on assets and these returns or instantaneous "growth rates" are stochastic.
Book
The theory of stochastic processes
David Cox,Hilton D. Miller +1 more
TL;DR: This book should be of interest to undergraduate and postgraduate students of probability theory.
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Lifetime Portfolio Selection By Dynamic Stochastic Programming
TL;DR: In this paper, the optimal consumption-investment problem for an investor whose utility for consumption over time is a discounted sum of single-period utilities, with the latter being constant over time and exhibiting constant relative risk aversion (power-law functions or logarithmic functions), is discussed.
Book
Stochastic Stability and Control
TL;DR: In this article, a book on stochastic stability and control dealing with Liapunov function approach to study of Markov processes is presented, which is based on the work of this article.
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