Abstract, classic, and explicit turnpikes
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Citation (published version)P. Guasoni, C. Kardaras, S. Robertson, H. Xing. 2014. "Abstract, classic, and explicit turnpikes." Finance and Stochastics, Volume 18, Issue 1, pp. 75 - 114. https://doi.org/10.1007/s00780-013-0216-5
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 turn- pikes. 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 un- der 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.