2017/08/12 by Mark Kelbert, Kelbert, Mark, Izabella Stuhl +3
Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1708.03813
openalex publication_date 2017/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, the logarithmic growth rate leads to a supermartingale, and (B) the optimal (martingale) investment strategy is a proportional betting. We focus on properties of the optimal portfolios and discuss a number of simple examples extending the well-known Kelly betting scheme. An important restriction is that the investment does not exceed the current capital value and allows the trader to cover the worst possible losses. The paper deals with a class of discrete-time models. A continuous-time extension is a topic of an ongoing study.