Stettner, Łukasz Discrete time infinite horizon risk sensitive portfolio selection with proportional transaction costs. (English) Zbl 1154.91479 Stettner, Łukasz (ed.), Advances in mathematics of finance. Contributed papers of the 2nd general AMaMeF (advanced mathematical methods of finance) conference and Banach Center conference on advances in mathematics of finance, Bȩdlewo, Poland, April 30–May 5, 2007. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 83, 231-241 (2008). Summary: Long run risk sensitive portfolio selection is considered with proportional transaction costs. In the paper two methods to prove existence of solutions to suitable Bellman equations are presented. The first method is based on discounted cost approximation and requires uniform absolute continuity of iterations of transition operators of the factor process. The second method is based on uniform ergodicity of portions of the capital invested in assets and requires additional assumptions concerning diversity of investments.For the entire collection see [Zbl 1151.91009]. Cited in 1 Document MSC: 91G10 Portfolio theory 93E20 Optimal stochastic control 91B30 Risk theory, insurance (MSC2010) Keywords:risk sensitive control; portfolio selection; proportional transaction costs; infinite horizon PDFBibTeX XMLCite \textit{Ł. Stettner}, Banach Cent. Publ. 83, 231--241 (2008; Zbl 1154.91479)