3 ms·
Kelly maximizes the median outcome, I think. I’ve yet to find an approach that minimize the bottom x percentile. If you’re aware of one I’d love to learn it.
by throwaway98797 6y ago
Kelly maximizes the median outcome, I think. I’ve yet to find an approach that minimize the bottom x percentile. If you’re aware of one I’d love to learn it.
- hntrader 6y agoI think you mean something that maximizes the bottom x percentile (either by making the negative smaller or the positive bigger). It's not going to be an easy solution, because for a sufficiently small x, the optimal strategy for a small number of bets is going to be to bet $0 each time (since the x-th percentile of the terminal outcome will be a loss on capital, or ruin), but the optimal strategy for a large number of bets is going to be to bet > $0 (since the x-th percentile of the terminal outcome will be positive). So we can already see that this is going to be a function of the number of bets, unlike with Kelly, and therefore is going to be a much harder problem.
- kgwgk 6y agoYou may find this interesting: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=439400 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=439400 “This paper provides an alternative behavioral foundation for an investor's use of power utility in the objective function and its particular risk aversion parameter. The foundation is grounded in an investor's desire to minimize the objective probability that the growth rate of invested wealth will not exceed an investor-selected target growth rate. Large deviations theory is used to show that this is equivalent to using power utility, with an argument that depends on the investor's target, and a risk aversion parameter determined by maximization. As a result, an investor's risk aversion parameter is not independent of the investment opportunity set, contrary to the standard model assumption.”