2014/08/27 by Huyen Pham, Pham, Huyen
Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #FOS: Mathematics #Portfolio Management (q-fin.PM) #Probability (math.PR) #math.PR #q-fin.PM
paper · pdf · doi:10.48550/arxiv.1408.6455
arxiv created 2014/08/27 · arxiv updated 2014/08/28
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 pro\-blems, 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.