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: The asset allocation of defined benefit pension plans of the type designed and sponsored by firms with the aim of providing a lifetime pension to the employees at the age of retirement is studied.
39 citations
TL;DR: In this paper, the authors build a structural model to assess the effect of these bonus restrictions and find that extended bonus accrual periods alone do not lead to lower risk-taking while a suffi ciently tight bonus cap does.
Abstract: Regulators restrict bankers' risk-taking incentives by using a bonus cap or by extending the effective bonus accrual period. We build a structural model to assess the effect of these bonus restrictions. The calibrated model suggests that extended bonus accrual periods alone do not lead to lower risk-taking while a suffi ciently tight bonus cap does. A bonus cap that equals fixed salary (as in the EU) reduces risk on average by 13%.
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TL;DR: In this article, the authors used the option approach to derive a theoretical model that shows the impact of policy uncertainty on investment in tradable quota in swine production in the Netherlands and provided weak evidence for the existence of option values due to policy uncertainty.
Abstract: Tradable permits are generally considered as an efficient instrument to regulate pollution by individual producers. However, uncertainty about changes in or possible discontinuation of the program could make individual farmers reluctant to invest in tradable permits. This article uses the option approach to derive a theoretical model that shows the impact of policy uncertainty on investment in tradable quota. The empirical assessment provides weak evidence for the existence of option values due to policy uncertainty for phosphate quota in swine production in the Netherlands.
39 citations
Cites result from "Optimum consumption and portfolio r..."
...In the specific case above where the Poisson event is that R falls permanently to zero, an increase in the jump probability is logically consistent with an increase in the discount rate, as shown by Merton (1971)....
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TL;DR: In this paper, the problem of maximizing expected logarithmic utility from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs is revisited, and a shadow price is derived for a frictionless price process with values in the bid-ask spread.
Abstract: We revisit the problem of maximizing expected logarithmic utility from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the seminal paper of Davis and Norman [Math. Operation Research, 15, 1990]. Similarly to Kallsen and Muhle-Karbe [Ann. Appl. Probab., 20, 2010], we tackle this problem by determining a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimization problem. However, we use a different parametrization, which facilitates computation and verification. Moreover, for small transaction costs, we determine fractional Taylor expansions of arbitrary order for the boundaries of the no-trade region and the value function. This extends work of Janecek and Shreve [Finance Stoch., 8, 2004], who determined the leading terms of these power series.
38 citations
TL;DR: Schwartz and Tebaldi as mentioned in this paper considered the problem of optimal asset location in a continuous time model, where one asset cannot be traded, and derived the value that the agent assigns to the illiquid asset, as well as contingent claims on those assets.
Abstract: Illiquid Assets and Optimal Portfolio Choice Eduardo S. Schwartz ∗ and Claudio Tebaldi † December 8, 2004 Abstract The presence of illiquid assets, such as human wealth, housing and proprietorships substantially complicates the problem of portfolio choice. This paper is concerned with the problem of optimal asset al- location in a continuous time model when one asset cannot be traded. This illiquid asset, which depends on an uninsurable source of risk, provides a liquid dividend. In the case of human capital we can think about this dividend as labor income. The agent is endowed with a given amount of the illiquid asset and with some liquid wealth which can be allocated in a market where there is a risky and a riskless as- set. The main point of the paper is that the optimal allocations to the two liquid assets and consumption will critically depend on the endowment and characteristics of the illiquid asset, in addition to the preferences and liquid wealth of the agent. We provide what we be- lieve to be the first analytical solution to this problem when the agent has power utility of consumption and terminal wealth. We also derive the value that the agent assigns to the illiquid asset. The risk adjusted valuation procedure we develop can be used to value both liquid and illiquid assets, as well as contingent claims on those assets. The Anderson School of Management, University of California at Los Angeles; 110 Westwood Plaza, Los Angeles, CA, 90095-1481 University of Verona and University of California at Los Angeles. Permanent Ad- dress: Universit` degli Studi di Verona, Dipartimento di Scienze Economiche, Via Giardino a Giusti, 2 - 37129 Verona, Italy. The present paper has been completed while the author was a visiting scholar at the Anderson School of Management, Faculty of Finance. C.T. gratefully acknowledges the Anderson School, the Finance Faculty and in particular Prof. Schwartz for the kind invitation and warm hospitality. C.T. would like to thank Marina Di Giacinto for constant support and many valuable comments, Martino Grasselli and the colleagues of the SAFE center in Verona for several insights and helpful discussions.
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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