Volume 57, Number 6, November-December 2023
|2981 - 3006
|30 November 2023
Optimal investment and consumption strategies for an investor with stochastic economic factor in a defaultable market
School of Economics and Statistics, Guangzhou University, Guangzhou 510006, P.R. China
* Corresponding author: email@example.com
Accepted: 6 September 2023
This paper considers the issue of optimal investment and consumption strategies for an investor with stochastic economic factor in a defaultable market. In our model, the price process is composed of a money market account and a default-free risky asset, assuming they rely on a stochastic economic factor described by a diffusion process. A defaultable perpetual bond is depicted by the reduced-form model, and both the default risk premium and the default intensity of it rely on the stochastic economic factor. Our goal is to maximize the infinite horizon expected discounted power utility of the consumption. Applying the dynamic programming principle, we derive the Hamilton–Jacobi–Bellman (HJB) equations and analyze them using the so-called sub-super solution method to prove the existence and uniqueness of their classical solutions. Next, we use a verification theorem to derive the explicit formula for optimal investment and consumption strategies. Finally, we provide a sensitivity analysis.
Mathematics Subject Classification: C58 / C61 / G11
Key words: Optimal control / stochastic economic factor / defaultable market / perpetual bond / sub-super solution
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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