Optimum consumption and portfolio rules in a continuous-time model☆
TL;DR: 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.
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TL;DR: In this article, the optimal proportional reinsurance and investment problem for an insurer in a defaultable market is analyzed, where the insurer can allocate his/her wealth among the following securities: a bank account, a risky stock asset and a corporate bond.
Abstract: This paper analyzes the optimal proportional reinsurance and investment problem for an insurer in a defaultable market. We assume that the reinsurance premium is calculated via the exponential premium principle. The insurer can allocate his/her wealth among the following securities: a bank account, a risky stock asset and a corporate bond. We decompose the original optimization problem into two sub-problems: a pre-default case and a post-default case. The optimal reinsurance and investment policies that maximize the expected CARA utility of the terminal wealth are explicitly derived. Numerical examples are given to illustrate our results, and we discuss relevant economic insights obtained from these results.
43 citations
TL;DR: In this paper, the authors developed an international C.A.M. including human capital, and underlined its contribution to the explanation of home bias observed in portfolio choice for nine countries.
43 citations
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TL;DR: In this paper, the authors show that such violations are more likely when future tax benefits are more volatile, which can occur, for example, when the tax rate differential across assets increases over time due either to tax law changes or to tax bracket changes for investors.
Abstract: Existing literature suggests that, in order to maximize the tax benefit of retirement accounts, investors should follow a "pecking order" location rule of placing highly taxed assets (e.g., bonds) in a tax-deferred account and lightly taxed assets (e.g., stocks) in a taxable account. Empirical evidence, however, documents that a large number of investors violate this rule. In this paper, we show that such violations can be optimal for risk-averse investors who face portfolio constraints. In particular, while the strategy of placing bonds in the tax-deferred account maximizes the expected level of tax benefit, it may lead to volatile benefits under different realizations of stock returns. By holding a similar portfolio in both accounts, investors can achieve amore balanced growth in the two accounts, minimize the likelihood of violating the constraints in the future, and hence "smooth" the volatility of the tax benefit. For some risk-averse investors, this smoothing motive can lead to the observed violation of the pecking order location rule. Our model predicts that such violations are more likely when future tax benefits are more volatile, which can occur, for example, when: (i) the tax rate differential across assets increases over time due either to tax law changes or to tax bracket changes for investors; (ii) asset returns are more volatile; and (iii) investors anticipate large future liquidity needs.
43 citations
TL;DR: In this paper, the authors investigated the problem of mean-variance portfolio choice with bankruptcy prohibition for incomplete markets with continuous assets' price processes and for complete markets, and they showed that the mean -variance efficient portfolios can be expressed as the optimal strategies of partial hedging for quadratic loss function.
Abstract: In this paper we investigate the problem of mean–variance portfolio choice with bankruptcy prohibition. For incomplete markets with continuous assets' price processes and for complete markets, it is shown that the mean–variance efficient portfolios can be expressed as the optimal strategies of partial hedging for quadratic loss function. Thus, mean–variance portfolio choice, in these cases, can be viewed as expected utility maximization with non-negative marginal utility.
43 citations
TL;DR: In this article, a new solution method for a broad class of discrete-time dynamic portfolio choice problems was developed, which efficiently approximates conditional expectations of the value function by using a decomposition of the state variables into a component observable by the investor and a stochastic deviation.
Abstract: We develop a new solution method for a broad class of discrete-time dynamic portfolio choice problems. The method efficiently approximates conditional expectations of the value function by using (i) a decomposition of the state variables into a component observable by the investor and a stochastic deviation; and (ii) a Taylor expansion of the value function. We illustrate the accuracy of the method in handling several realistic features of portfolio choice problems such as intermediate consumption, multiple assets, multiple state variables, portfolio constraints, non-time-separable preferences, and nonredundantendogenous state variables. We finally use the method to solve a realistic large-scale life-cycle portfolio choice and consumption problem with predictable expected returns and recursive preferences. (JEL G11, G12)
43 citations
Cites background from "Optimum consumption and portfolio r..."
...Since the seminal work of Samuelson (1969) and Merton (1969, 1971) , the study of portfolio formation and manage-...
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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.
Abstract: OST models of portfolio selection have M been one-period models. I examine the combined problem of optimal portfolio selection and consumption rules for an individual in a continuous-time model whzere his income is generated by returns on assets and these returns or instantaneous "growth rates" are stochastic. P. A. Samuelson has developed a similar model in discrete-time for more general probability distributions in a companion paper [8]. I derive the optimality equations for a multiasset problem when the rate of returns are generated by a Wiener Brownian-motion process. A particular case examined in detail is the two-asset model with constant relative riskaversion or iso-elastic marginal utility. An explicit solution is also found for the case of constant absolute risk-aversion. The general technique employed can be used to examine a wide class of intertemporal economic problems under uncertainty. In addition to the Samuelson paper [8], there is the multi-period analysis of Tobin [9]. Phelps [6] has a model used to determine the optimal consumption rule for a multi-period example where income is partly generated by an asset with an uncertain return. Mirrless [5] has developed a continuous-time optimal consumption model of the neoclassical type with technical progress a random variable.
4,908 citations
Book•
01 Jan 1965
TL;DR: This book should be of interest to undergraduate and postgraduate students of probability theory.
Abstract: This book should be of interest to undergraduate and postgraduate students of probability theory.
3,597 citations
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.
Abstract: Publisher Summary This chapter reviews 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). It presents a generalization of Phelps' model to include portfolio choice and consumption. The explicit form of the optimal solution is derived for the special case of utility functions having constant relative risk aversion. The optimal portfolio decision is independent of time, wealth, and the consumption decision at each stage. Most analyses of portfolio selection, whether they are of the Markowitz–Tobin mean-variance or of more general type, maximize over one period. The chapter only discusses special and easy cases that suffice to illustrate the general principles involved and presents the lifetime model that reveals that investing for many periods does not itself introduce extra tolerance for riskiness at early or any stages of life.
2,369 citations
Book•
17 Jan 2012
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.
Abstract: Book on stochastic stability and control dealing with Liapunov function approach to study of Markov processes
1,293 citations
987 citations