On the Bellman equation for asymptotics of utility from terminal wealth

Volume 37 / 2010

Janusz Matkowski, Łukasz Stettner Applicationes Mathematicae 37 (2010), 89-97 MSC: Primary 91G10; Secondary 93E20. DOI: 10.4064/am37-1-6

Abstract

The asymptotics of utility from terminal wealth is studied. First, a finite horizon problem for any utility function is considered. To study a long run infinite horizon problem, a certain positive homogeneity (PH) assumption is imposed. It is then shown that assumption (PH) is practically satisfied only by power and logarithmic utility functions.

Authors

  • Janusz MatkowskiInstitute of Mathematics,
    Computer Science and Econometrics
    University of Zielona Góra
    Podgórna 50
    65-246 Zielona Góra, Poland
    and
    Institute of Mathematics
    Silesian University
    40-007 Katowice, Poland
    e-mail
  • Łukasz StettnerInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland
    and
    Academy of Finance
    e-mail

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