Consumption Investment Problem
The consumer-investment problem is a standard problem in modern financial economics . It raises the question of how a risk-averse consumer should invest his available financial and human capital intertemporally over his life cycle and how much he should consume at any point in time (i.e. how high his savings rate should be and which portfolio he should choose for his fixed assets). It can be represented as a stochastic optimization problem via a continuous Brownian movement and was solved in its basic form in 1969 by Robert C. Merton for foundations with a fixed and an infinite lifespan using the Itō's lemma . A key insight into Merton's model is that an investor with a standard CRRA utility function is “short term”; long-term investment does not reduce risks. It also shows that the Tobin separation can be maintained. In the model, risk is expressed specifically in the fact that the savings rate and thus the capital available for consumption fluctuates with the capital market: If the capital market generates losses, the savings rate must be increased and vice versa. It is no longer just an abstract fluctuation in the size of wealth. The Mertons model thus overcomes the deficits of the capital goods price model . Refinements to the model take into account transaction costs, retirement age, bankruptcy, human life cycles (i.e., stochastic mortality), and other factors. Merton's model has become the standard model for rational, life-cycle financial planning.
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- ^ Robert C. Merton: Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case. Rev Econ Stat 51: 3 (1969), pp. 247-257
- ^ Paul Samuelson: Lifetime Portfolio Selection By Dynamic Stochastic Programming. Rev Econ Stat 51: 3 (1969), pp. 239-246
- ^ Zvi Bodie: Overview . The Future of Life-Cycle Saving and Investing (February 2008), 2nd Edition, pp. Xviii.