Abstract, Classic, and Explicit Turnpikes

Details Abstract, Classic, and Explicit Turnpikes Abstract, Classic, and Explicit Turnpikes

2011-01-05

arxiv.org/abs/1101.0945v2

Economy

Quantitative Finance

Portfolio Management

36 pages. Revised version. Certain technical conditions on utility have been removed and a new example has been added

Scientific paper

Portfolio turnpikes state that, as the investment horizon increases, optimal portfolios for generic utilities converge to those of isoelastic utilities. This paper proves three kinds of turnpikes. In a general semimartingale setting, the abstract turnpike states that optimal final payoffs and portfolios converge under their myopic probabilities. In diffusion models with several assets and a single state variable, the classic turnpike demonstrates that optimal portfolios converge under the physical probability; meanwhile the explicit turnpike identifies the limit of finite-horizon optimal portfolios as a long-run myopic portfolio defined in terms of the solution of an ergodic HJB equation.

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