Robust utility maximizing strategies under model uncertainty and their convergence

Sass, Jörn; Westphal, Dorothee

doi:10.1007/s11579-022-00312-w

Cited by 2 publications

(1 citation statement)

References 28 publications

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“…We leave it to future studies to clarify under which conditions on A the value functions in Equations (53) and (54) actually coincide, including whether the set

A=(\gamma _1,\gamma _2)

actually fulfills such conditions. To this end, ideas exploited in Sass and Westphal (2022) for the case of an uncertain drift, have to be properly adapted to the case of a random risk aversion. Moreover, it is encouraging that Balter and Schweizer (2021) find that Equations (53) and (54) coincide in their one‐period model.…”

Section: Relation To Other Approaches and Outlookmentioning

confidence: 99%

Equilibrium investment with random risk aversion

Desmettre

Steffensen

2023

Mathematical Finance

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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. K E Y W O R D Scertainty equivalents, equilibrium approach, power and exponential utility, random risk aversion, time-inconsistency INTRODUCTIONWe formulate and solve a dynamic portfolio optimization problem under random preferences by taking a distribution over certainty equivalents. This forms a new approach to optimization under random preferences. The problem becomes time-inconsistent and we deal with this via the equilibrium approach. The elegance of the solution is demonstrated for standard choices of preferences like power (constant relative risk aversion) and exponential (constant absolute riskThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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“…We leave it to future studies to clarify under which conditions on A the value functions in Equations (53) and (54) actually coincide, including whether the set

A=(\gamma _1,\gamma _2)

Section: Relation To Other Approaches and Outlookmentioning

confidence: 99%

Equilibrium investment with random risk aversion

Desmettre

Steffensen

2023

Mathematical Finance

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Optimal Investment Strategy for α-Robust Utility Maximization Problem

Yang,

Li,

Zeng

et al. 2024

Mathematics of OR

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In reality, investors are uncertain about the dynamics of risky asset returns. Therefore, investors prefer to make robust investment decisions. In this paper, we propose an α-robust utility maximization problem under uncertain parameters. The investor is allowed to invest in a financial market consisting of a risk-free asset and a risky asset. The uncertainty about the expected return rate is parameterized by a nonempty set. Different from most existing literature on robust utility maximization problems where investors are generally assumed to be extremely ambiguity averse because they tend to consider only expected utility in the worst-case scenario, we pay attention to the investors who are not only ambiguity averse but also ambiguity seeking. Under power utility, we provide the implicit function representations for the precommitted strategy, equilibrium strategy of the open-loop type, and equilibrium strategy of the closed-loop type. Some properties about the optimal trading strategies, the best-case and worst-case parameters under three different kinds of strategies, are provided. Funding: This work was supported by National Natural Science Foundation of China [Grants 12071147, 12171169, 12271171, 12371470, 71721001, 71931004, 72371256], the Shanghai Philosophy Social Science Planning Office Project [Grant 2022ZJB005], Fundamental Research Funds for the Central Universities [Grant 2022QKT001], the Excellent Young Team Project Natural Science Foundation of Guangdong Province of China [Grant 2023B1515040001], the Philosophy and Social Science Programming Foundation of Guangdong Province [Grant GD22CYJ17], the Nature Science Foundation of Guangdong Province of China [Grant 2022A1515011472], and the 111 Project [Grant B14019].

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Robust utility maximizing strategies under model uncertainty and their convergence

Cited by 2 publications

References 28 publications

Equilibrium investment with random risk aversion

Equilibrium investment with random risk aversion

Optimal Investment Strategy for α-Robust Utility Maximization Problem

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