Equilibrium investment with random risk aversion
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Equilibrium investment with random risk aversion. / Desmettre, Sascha; Steffensen, Mogens.
In: Mathematical Finance, Vol. 33, No. 3, 2023, p. 946-975.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Equilibrium investment with random risk aversion
AU - Desmettre, Sascha
AU - Steffensen, Mogens
N1 - Publisher Copyright: © 2023 The Authors. Mathematical Finance published by Wiley Periodicals LLC.
PY - 2023
Y1 - 2023
N2 - We solve the problem of an investor who maximizes utility but faces random preferences. We propose a problem formulation based on expected certainty equivalents. We tackle the time-consistency issues arising from that formulation by applying the equilibrium theory approach. To this end, we provide the proper definitions and prove a rigorous verification theorem. We complete the calculations for the cases of power and exponential utility. For power utility, we illustrate in a numerical example that the equilibrium stock proportion is independent of wealth, but decreasing in time, which we also supplement by a theoretical discussion. For exponential utility, the usual constant absolute risk aversion is replaced by its expectation.
AB - We solve the problem of an investor who maximizes utility but faces random preferences. We propose a problem formulation based on expected certainty equivalents. We tackle the time-consistency issues arising from that formulation by applying the equilibrium theory approach. To this end, we provide the proper definitions and prove a rigorous verification theorem. We complete the calculations for the cases of power and exponential utility. For power utility, we illustrate in a numerical example that the equilibrium stock proportion is independent of wealth, but decreasing in time, which we also supplement by a theoretical discussion. For exponential utility, the usual constant absolute risk aversion is replaced by its expectation.
KW - certainty equivalents
KW - equilibrium approach
KW - power and exponential utility
KW - random risk aversion
KW - time-inconsistency
UR - http://www.scopus.com/inward/record.url?scp=85158084372&partnerID=8YFLogxK
U2 - 10.1111/mafi.12394
DO - 10.1111/mafi.12394
M3 - Journal article
C2 - 38505113
AN - SCOPUS:85158084372
VL - 33
SP - 946
EP - 975
JO - Mathematical Finance
JF - Mathematical Finance
SN - 0960-1627
IS - 3
ER -
ID: 358724825