Mortality and Healthcare: A Stochastic Control Analysis under Epstein--Zin Preferences

Aurand, Joshua; Huang, Yu‐Jui

doi:10.1137/20m1331111

Cited by 2 publications

(1 citation statement)

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“…It is of interest to consider more general random horizons 𝜏 that are not limited to the market filtration. The companion paper Aurand and Huang (2021) pursued this direction: it studies optimal consumption, investment, and healthcare spending under Epstein-Zin preferences over an agent's random lifetime; namely, 𝜏 is the death time of the agent, which need not depend on the financial market.…”

Section: Introductionmentioning

confidence: 99%

Epstein‐Zin utility maximization on a random horizon

Aurand

Huang

2023

Mathematical Finance

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This paper solves the consumption‐investment problem under Epstein‐Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do not impose any fixed upper bound for the random horizon, allowing for truly unbounded ones. Focusing on the empirically relevant case where the risk aversion and the elasticity of intertemporal substitution are both larger than one, we characterize the optimal consumption and investment strategies using backward stochastic differential equations with superlinear growth on unbounded random horizons. This characterization, compared with the classical fixed‐horizon result, involves an additional stochastic process that serves to capture the randomness of the horizon. As demonstrated in two concrete examples, changing from a fixed horizon to a random one drastically alters the optimal strategies.

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Section: Introductionmentioning

confidence: 99%

Epstein‐Zin utility maximization on a random horizon

Aurand

Huang

2023

Mathematical Finance

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Stability of the Epstein–Zin problem

Monoyios,

Mostovyi

2024

Mathematical Finance

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We investigate the stability of the Epstein–Zin problem with respect to small distortions in the dynamics of the traded securities. We work in incomplete market model settings, where our parametrization of perturbations allows for joint distortions in returns and volatility of the risky assets and the interest rate. Considering empirically the most relevant specifications of risk aversion and elasticity of intertemporal substitution, we provide a condition that guarantees the convexity of the domain of the underlying problem and results in the existence and uniqueness of a solution to it. Then, we prove the convergence of the optimal consumption streams, the associated wealth processes, the indirect utility processes, and the value functions in the limit when the model perturbations vanish.

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Mortality and Healthcare: A Stochastic Control Analysis under Epstein--Zin Preferences

Cited by 2 publications

References 29 publications

Epstein‐Zin utility maximization on a random horizon

Epstein‐Zin utility maximization on a random horizon

Stability of the Epstein–Zin problem

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