Merton's portfolio problem

The life cycle model is the standard model of modern financial planning Economics.

It answers the question of how a risk-averse consumer invest its available financial and human capital intertemporally and how much he should verkonsumieren at any time (ie, how much should its savings rate, and what should be the part he risky and he certainly invests). The basic problem can be represented as a stochastic optimization problem on a continuous Brownian motion and was dissolved in its basic form in 1969 by Robert C. Merton for foundations with fixed and with infinite life using the Lemma of Itō. A central insight of the model is that an investor with standard CRRA utility function " short-term" applies; long-term investment risks does not lower. Furthermore, it follows that the Tobin separation can be maintained. Risk manifests itself in the model concretely is that the savings rate and hence available for the consumption of capital varies with the capital market ( made ​​in capital market losses, the savings rate has to be increased and vice versa), and not only in the abstract as a variation in the size of the assets. The life-cycle model thereby overcomes the shortcomings of Kapitalgutpreismodells. Refinements of the model take into account transaction costs, retirement choice, insolvency, human typical life cycles (ie stochastic mortality) and other factors.

Swell

• Financing