Equilibrium investment with random risk aversion

Institut for Matematiske Fag

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Standard

Equilibrium investment with random risk aversion. / Desmettre, Sascha; Steffensen, Mogens.

I: Mathematical Finance, Bind 33, Nr. 3, 2023, s. 946-975.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Desmettre, S & Steffensen, M 2023, 'Equilibrium investment with random risk aversion', Mathematical Finance, bind 33, nr. 3, s. 946-975. https://doi.org/10.1111/mafi.12394

APA

Desmettre, S., & Steffensen, M. (2023). Equilibrium investment with random risk aversion. Mathematical Finance, 33(3), 946-975. https://doi.org/10.1111/mafi.12394

Vancouver

Desmettre S, Steffensen M. Equilibrium investment with random risk aversion. Mathematical Finance. 2023;33(3):946-975. https://doi.org/10.1111/mafi.12394

Author

Desmettre, Sascha ; Steffensen, Mogens. / Equilibrium investment with random risk aversion. I: Mathematical Finance. 2023 ; Bind 33, Nr. 3. s. 946-975.

Bibtex

@article{771fdf893d4949c2aeed55de8d251cc6,

title = "Equilibrium investment with random risk aversion",

abstract = "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.",

keywords = "certainty equivalents, equilibrium approach, power and exponential utility, random risk aversion, time-inconsistency",

author = "Sascha Desmettre and Mogens Steffensen",

note = "Publisher Copyright: {\textcopyright} 2023 The Authors. Mathematical Finance published by Wiley Periodicals LLC.",

year = "2023",

doi = "10.1111/mafi.12394",

language = "English",

volume = "33",

pages = "946--975",

journal = "Mathematical Finance",

issn = "0960-1627",

publisher = "Wiley-Blackwell",

number = "3",

}

RIS

TY - JOUR

T1 - Equilibrium investment with random risk aversion

AU - Desmettre, Sascha

AU - Steffensen, Mogens

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