We consider a non-consuming agent investing in a stock and a money market interested in the portfolio market price far in the future. We derive a strategy which is almost log-optimal in the long run in the presence of small proportional transaction costs for the case when the rate of return and the volatility of the stock market price are bounded It\^o processes with bounded coefficients and when the volatility is bounded away from zero.
Článek přibližuje výsledky interdisciplinárního výzkumu spontánních procesů spojených se změnou biodiverzity v průběhu osidlování toxických substrátů (rudná/strusko-popílková odkaliště) různými skupinami organismů od mikroskopických hub, přes půdní řasy, lišejníky, mechy, až po byliny a porosty dřevin a na ně vázanými bezobratlými i obratlovci, jako jsou např. roztoči, mšice, mravenci, pískomilné druhy hmyzu, někteří ptáci a savci. Na základě praktických výsledků výzkumu byly formulovány návrhy, jak s nízkými náklady obnovit vegetaci těchto antropogenně vzniklých stanovišť. and This article emphasizes the interdisciplinary study of spontaneous processes related to biodiversity changes during colonization of toxic substrates (ore/ash slag deposits) by different groups of organisms, from microscopic fungi, soil algae, lichens, and mosses to herb and woody stands with their associated invertebrates and vertebrates, such as mites, aphids, ants, psammophilous insects, some birds and mammals. The practical results of these studies include suggestions on how to restore the vegetation on these non-natural bodies at a minimum cost.
We consider a non-consuming agent interested in the maximization of the long-run growth rate of a wealth process investing either in a money market and in one risky asset following a geometric Brownian motion or in futures following an arithmetic Brownian motion. The agent faces proportional transaction costs, and similarly as in [17] where the case of stock trading is considered, we show how the log-optimal optimal policies in the long run can be derived when using the technical tool of shadow prices. We also provide a brief link between technical tools used in this paper and the ones used in [14,15,17].