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

Published online by Cambridge University Press:  23 January 2023

Mogens Steffensen  and
Julie Bjørner Søe Open the ORCID record for Julie Bjørner Søe [Opens in a new window]
Mogens Steffensen
Affiliation:
Department of Mathematical Sciences, University of Copenhagen. Universitetsparken 5, 2100 København, Denmark
Julie Bjørner Søe*
Affiliation:
Department of Mathematical Sciences, University of Copenhagen. Universitetsparken 5, 2100 København, Denmark Mancofi A/S, Carl Jacobsens Vej 20, 2500 København, Denmark
*
*Corresponding author. E-mail: js@math.ku.dk
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Abstract

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.

Keywords

Multistate modelsthe disability modelstate-dependent utilityHamilton–Jacobi–Bellman equation

Information

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 53 , Issue 1 , January 2023 , pp. 104 - 128
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The International Actuarial Association

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