# Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case

@article{Merton1969LifetimePS, title={Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case}, author={R. C. Merton}, journal={The Review of Economics and Statistics}, year={1969}, volume={51}, pages={247-257} }

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… Expand

#### Figures from this paper

#### 4,511 Citations

Optimum Consumption and Portfolio Rules in a Continuous-Time Model*

- Mathematics, Economics
- 1975

Publisher Summary
A common hypothesis about the behavior of limited liability asset prices in perfect markets is the random walk of returns or in its continuous-time form the geometric Brownian… Expand

Incorporating Estimation Error into Optimal Portfolio allocation

- Economics
- 2006

In this report, we consider the problem concerned with incorporating estimation error into optimal consumption and portfolio selection in continuous time. The original optimal consumption and asset… Expand

Consumption and portfolio rules for time-inconsistent investors

- Mathematics, Computer Science
- Eur. J. Oper. Res.
- 2010

This paper extends the classical consumption and portfolio rules model in continuous time to the framework of decision-makers with time-inconsistent preferences and derives a modified HJB (Hamilton-Jacobi-Bellman) equation to solve the problem for sophisticated agents. Expand

Optimal portfolios for DC pension plans under a CEV model

- Economics
- 2009

This paper studies the portfolio optimization problem for an investor who seeks to maximize the expected utility of the terminal wealth in a DC pension plan. We focus on a constant elasticity of… Expand

Time-Consistent Portfolio Management

- Economics, Computer Science
- SIAM J. Financial Math.
- 2012

This paper considers the portfolio management problem for an investor with finite time horizon who is allowed to consume and take out life insurance. Natural assumptions, such as different discount… Expand

A renewal theoretic result in portfolio theory under transaction costs with multiple risky assets

- Economics
- 2009

We consider a portfolio optimization problem in a Black-Scholes model with n stocks, in which an investor faces both fixed and proportional transaction costs. The performance of an investment… Expand

An Explicit Solution for a Portfolio Selection Problem with Stochastic Volatility

- Economics
- 2017

In this paper, we revisit the optimal consumption and portfolio selection problem for an investor who has access to a risk-free asset (e.g. bank account) with constant return and a risky asset (e.g.… Expand

Optimal Portfolio and Consumption Decisions in a Stochastic Environment with Precommitment

- Economics
- 1995

In this paper we solve the stochastic portfolios-consumption control problem under the assumption that individuals follow precommitment strategies over finite intervals of time. This precommitment… Expand

Continuous Time Mean-Variance Portfolio Selection Problem

- Economics
- 2008

This thesis is devoted to Markowitz's mean-variance portfolio selection problem in continuous time financial markets, where we aim to minimise the risk of the investment, which is expressed by the… Expand

Optimal portfolios with regime switching and value-at-risk constraint

- Mathematics, Computer Science
- Autom.
- 2010

We consider the optimal portfolio selection problem subject to a maximum value-at-Risk (MVaR) constraint when the price dynamics of the risky asset are governed by a Markov-modulated geometric… Expand

#### References

SHOWING 1-7 OF 7 REFERENCES

THE ACCUMULATION OF RISKY CAPITAL: A SEQUENTIAL UTILITY ANALYSIS

- Economics
- 1962

This chapter discusses the optimal lifetime consumption strategy of an individual whose wealth holding possibilities expose him to the risk of loss. The vehicle of analysis is a stochastic,… Expand

Mr. Harrod on Hump Saving

- Economics
- 1950

"The fundamental theory of the supply of saving", says Mr. Harrod,1 " may be set out in the form of equations ". This note is concerned with the particular form in which Mr. Harrod proceeds to set… Expand

Dynamic Programming and the Calculus of Variations (New York

- 1965

Optimum Accumulation Under Uncertainty

- Optimum Accumulation Under Uncertainty
- 1965

The Theory of Portfolio Selection The Theory of Interest Rates

- The Theory of Portfolio Selection The Theory of Interest Rates
- 1965

Mr. Harrod on Hump Saving Economica

- Mr. Harrod on Hump Saving Economica
- 1950