2015/05/06 by Yuri Suhov, Suhov, Y., Izabella Stuhl +3 · 1 citation
Economics, Econometrics and Finance · Decision Sciences · #Economic theories and models #Stochastic processes and financial applications #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.1505.01437
Following the paper by Algoet--Cover (1988), we analyse log-optimal portfolios where return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, logarithmic growth rate is a supermartingale, and (B) the optimal (martingale) investment strategy is a proportional betting; it does not depend on the form of the weight function, although the optimal rate does. The existence of an optimal investment strategy has been established earlier in a great generality by Kramkov--Schachermayer (2003) although our underlying assumptions are different.