TY - JOUR

T1 - Optimal consumption, investment, and insurance under state-dependent risk aversion

AU - Steffensen, Mogens

AU - Soe, Julie Bjorner

N1 - Publisher Copyright: © The Author(s), 2023. Published by Cambridge University Press on behalf of The International Actuarial Association.

PY - 2023

Y1 - 2023

N2 - We formalize a consumption-investment-insurance problem with the distinction of a state-dependent relative risk aversion. The state dependence refers to the state of the finite state Markov chain that also formalizes insurable risks such as health and lifetime uncertainty. We derive and analyze the implicit solution to the problem, compare it with special cases in the literature, and illustrate the range of results in a disability model where the relative risk aversion is preserved, decreases, or increases upon disability.

AB - We formalize a consumption-investment-insurance problem with the distinction of a state-dependent relative risk aversion. The state dependence refers to the state of the finite state Markov chain that also formalizes insurable risks such as health and lifetime uncertainty. We derive and analyze the implicit solution to the problem, compare it with special cases in the literature, and illustrate the range of results in a disability model where the relative risk aversion is preserved, decreases, or increases upon disability.

KW - Hamilton-Jacobi-Bellman equation

KW - Multistate models

KW - state-dependent utility

KW - the disability model

UR - http://www.scopus.com/inward/record.url?scp=85149929538&partnerID=8YFLogxK

U2 - 10.1017/asb.2022.25

DO - 10.1017/asb.2022.25

M3 - Journal article

AN - SCOPUS:85149929538

VL - 53

SP - 104

EP - 128

JO - ASTIN Bulletin: The Journal of the IAA

JF - ASTIN Bulletin: The Journal of the IAA

SN - 0515-0361

IS - 1

ER -