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Abstract, classic, and explicit turnpikes. (English) Zbl 1303.91157

Summary: 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. In the same setting, 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.

MSC:

91G10 Portfolio theory
93E20 Optimal stochastic control
60H30 Applications of stochastic analysis (to PDEs, etc.)
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