This survey reviews portfolio selection problem for long-term horizon. We consider two objectives: (i) maximize the probability for outperforming a target growth rate of wealth process (ii) minimize the probability of falling below a target growth rate. We study the asymptotic behavior of these criteria formulated as large deviations control problems, that we solve by duality method leading to ergodic risk-sensitive portfolio optimization problems. Special emphasis is placed on linear factor models where explicit solutions are obtained.
CITATION STYLE
Pham, H. (2015). Long time Asymptotics for optimal investment. In Springer Proceedings in Mathematics and Statistics (Vol. 110, pp. 507–528). Springer New York LLC. https://doi.org/10.1007/978-3-319-11605-1_18
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