Polynomial Utility
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Polynomial Utility. / Lollike, Alexander S.; Steffensen, Mogens.
I: International Journal of Theoretical and Applied Finance, Bind 26, Nr. 06n07, 2350024, 2023.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Polynomial Utility
AU - Lollike, Alexander S.
AU - Steffensen, Mogens
N1 - Publisher Copyright: ©c World Scientific Publishing Company.
PY - 2023
Y1 - 2023
N2 - We approximate the utility function by polynomial series and solve the related dynamic portfolio optimization problems. We study the quality of the Taylor and Bernstein series approximation in response to the points and degrees of the expansions and generalize from earlier expansions applied to portfolio optimization. The issue of time inconsistency, arising from a dynamically adapted center of the expansion, is approached by equilibrium theory. We present new ways of constructing polynomial utility functions and study their pitfalls and potentials. In the numerical study, we focus on two specific utility functions: For power utility, access to the optimal portfolio allows for a complete illustration of the approximations; for the S-shaped utility function of prospect theory, the use of equilibrium theory allows for approximating the solution to the (obviously interesting but yet unsolved) case of current wealth as a dynamic reference point.
AB - We approximate the utility function by polynomial series and solve the related dynamic portfolio optimization problems. We study the quality of the Taylor and Bernstein series approximation in response to the points and degrees of the expansions and generalize from earlier expansions applied to portfolio optimization. The issue of time inconsistency, arising from a dynamically adapted center of the expansion, is approached by equilibrium theory. We present new ways of constructing polynomial utility functions and study their pitfalls and potentials. In the numerical study, we focus on two specific utility functions: For power utility, access to the optimal portfolio allows for a complete illustration of the approximations; for the S-shaped utility function of prospect theory, the use of equilibrium theory allows for approximating the solution to the (obviously interesting but yet unsolved) case of current wealth as a dynamic reference point.
KW - Dynamic programming
KW - expected utility theory
KW - optimal asset allocation
KW - polynomial expansions
U2 - 10.1142/S0219024923500243
DO - 10.1142/S0219024923500243
M3 - Journal article
AN - SCOPUS:85181453473
VL - 26
JO - International Journal of Theoretical and Applied Finance
JF - International Journal of Theoretical and Applied Finance
SN - 0219-0249
IS - 06n07
M1 - 2350024
ER -
ID: 382974507