Time-consistent asset allocation for risk measures in a Lévy market

Felix Fießinger and Mitja Stadje

European Journal of Operational Research, 2025, vol. 321, issue 2, 676-695

Abstract: Focusing on gains & losses relative to a risk-free benchmark instead of terminal wealth, we consider an asset allocation problem to maximize time-consistently a mean-risk reward function with a general risk measure which is (i) law-invariant, (ii) cash- or shift-invariant, and (iii) positively homogeneous, and possibly plugged into a general function. Examples include (relative) Value at Risk, coherent risk measures, variance, and generalized deviation risk measures. We model the market via a generalized version of the multi-dimensional Black–Scholes model using α-stable Lévy processes and give supplementary results for the classical Black–Scholes model. The optimal solution to this problem is a Nash subgame equilibrium given by the solution of an extended Hamilton–Jacobi–Bellman equation. Moreover, we show that the optimal solution is deterministic under appropriate assumptions.

Keywords: Decision analysis; Jump process; Time-consistency; Optimal investment; Hamilton–Jacobi–Bellman equation (search for similar items in EconPapers)
JEL-codes: C61 C72 C73 D52 G11 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:321:y:2025:i:2:p:676-695

DOI: 10.1016/j.ejor.2024.09.049

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