CONTENTS1. Introduction........................................................................................................ 52. Preliminary results and assumptions.................................................................. 73. Approximation of the invariant measure.............................................................. 144. Construction of nearly optimal control functions................................................ 24 4.1. Approximation of admissible control functions.....................................
Optimal control with long run average cost functional of a partially observed Markov process is considered. Under the assumption that the transition probabilities are equivalent, the existence of the solution to the Bellman equation is shown, with the use of which optimal strategies are constructed.
Risk sensitive and risk neutral long run portfolio problems with consumption and proportional transaction costs are studied. Existence of solutions to suitable Bellman equations is shown. The asymptotics of the risk sensitive cost when the risk factor converges to 0 is then considered. It turns out that optimal strategies are stationary functions of the portfolio (portions of the wealth invested in assets) and of economic factors. Furthermore an optimal portfolio strategy for a risk neutral control...
We study the asymptotical behaviour of expected utility from terminal wealth on a market in which asset prices depend on economic factors that are unobserved or observed with delay.
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...
The 47th National Conference on Mathematics Applications was held on September 4-11, 2018 in Zakopane Kościelisko. Together with the conference, the XXIV National Conference on Mathematics Applications in Biology and Medicine (4-7 September 2018) was held simultaneously with two common first days of the meeting. The plenary lecture was delivered by Urszula Ledzewicz (Southern Illinois University Edwardsville, USA and Łódź University of Technology) and Heinz Schättler (Washington University, St....
Kolejna XLV Konferencja Zastosowań skupiła 99 uczestników co jest nieco więcej niż w roku poprzednim. W czasie konferencji wygłoszono 26 dłuższych wykładów (co najmniej 40 minutowych) w tym dwuczęściowy wykład prof. Wiesława Dziubdzieli poświęcony asymptotyce rozkładów ekstremalnych i rekordowych oraz 30 komunikatów i 18 plakatów. Wykład inauguracyjny pt. „Statystyczne metody lokalizacji genów odpowiedzialnych za istotne charakterystyki” wygłosiła prof. Małgorzata Bogdan. Na uwagę zasługują też...
For some time, in teams of mathematicians who are accustomed to its applications, in Poland, there is a debate over the need for the appointment of a new discipline within the mathematical sciences that would be the application of mathematics. Because I belong to the supporters of such a solution I do attempt to present arguments that lead me to this attitude.
Doc Dr. Eugene Fidelis was born on August 30, 1927 in Plonsk. By 1939, he completed six years of primary school. After the occupation he attended middle school and high school for adults in Plock while working at the district office, first as an office assistant, clerk later to finally come to the position of director of the office of law and administrative. In 1949 he entered the Faculty of Mathematics and Natural Sciences, the University...
Kolejny już ósmy Kongres ICIAM (The International Council for Industrial and Applied Mathematics) tym razem zagościł w kraju środka. Był to zdecydowanie największy z dotychczasowych kongresów. Uczestniczyło w nim ponad 3400 naukowców. Obrady odbywały się w części ogromnego Convention Center. Na inauguracje Kongresu przybył Vice Prezydent Chińskiej Republiki Ludowej Li Yuanchao, który z wykształcenia jest matematykiem po Fudan University. Kongres ICIAMu był ostatnim kongresem prezydenta ICIAMu Barbary...
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The 47th National Conference on Mathematics Applications was held on September 4-11, 2018 in Zakopane Kościelisko. Together with the conference, the XXIV National Conference on Mathematics Applications in Biology and Medicine (4-7 September 2018) was held simultaneously with two common first days of the meeting. The plenary lecture was delivered by Urszula Ledzewicz (Southern Illinois University Edwardsville, USA and Łódź University of Technology) and Heinz Schättler (Washington University, St....
On March 23, 2018 in Warsaw, at the seat of the Mathematical Institute of the Polish Academy of Sciences, a solemn scientific session was held to commemorate the 15th anniversary of the Center for Applied Mathematics (CZM) IMPAN and the 65th anniversary of the Applicationes Mathematicae scientific journal. The history of CZM and Applicationes was reminded by Łukasz Stettner, CZM manager and editor-in-chief Applicationes. The Application Center for Mathematics was created on the 50th anniversary...
Vancouver 17–22 of July 2011
Two adaptive procedures for controlled Markov chains which are based on a nonparametric window estimation are shown.
Option pricing in the multidimensional case, i.e. when the contingent claim paid at maturity depends on a number of risky assets, is considered. It is assumed that the prices of the risky assets are in discrete time subject to binomial disturbances. Two approaches to option pricing are studied: geometric and analytic. A numerical example is also given.
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