Geodesic
On the Bellman equation for asymptotics of utility from terminal wealth
Janusz Matkowski1 ; Łukasz Stettner2
1 Institute 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
2 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland and Academy of Finance
Applicationes Mathematicae, Tome 37 (2010) no. 1, pp. 89-97 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am37-1-6
Keywords: asymptotics utility terminal wealth studied first finite horizon problem utility function considered study long run infinite horizon problem certain positive homogeneity assumption imposed shown assumption practically satisfied only power logarithmic utility functions

Janusz Matkowski 1 ; Łukasz Stettner 2

1 Institute 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
2 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland and Academy of Finance 
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Janusz Matkowski; Łukasz Stettner. On the Bellman equation for asymptotics of
 utility from terminal wealth. Applicationes Mathematicae, Tome 37 (2010) no. 1, pp. 89-97. doi: 10.4064/am37-1-6

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