Open AccessRobust optimal asset-liability management with penalization on ambiguity
Author(s) -
Yu Yuan,
Hui Mi
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2021121
Subject(s) - ambiguity , bellman equation , hamilton–jacobi–bellman equation , dynamic programming , mathematics , mathematical economics , investment strategy , asset (computer security) , mathematical optimization , investment (military) , computer science , economics , finance , computer security , market liquidity , political science , law , programming language , politics
In this paper, we study the robust optimal asset- problems for an ambiguity-averse investor, who does not have perfect information in the drift terms of the risky asset and liability processes. Two different kinds of objectives are considered: \begin{document}$ (i) $\end{document} Maximizing the minimal expected utility of the terminal wealth; \begin{document}$ (ii) $\end{document} Minimizing the maximal cumulative deviation. The ambiguity in both problems is described by a set of equivalent measures to the reference model. By the stochastic dynamic programming approach and Hamilton-Jacobi-Bellman (HJB) equation, we derive closed-form expressions for the value function and corresponding robust optimal investment strategy in each problem. Furthermore, some special cases are provided to investigate the effect of model uncertainty on the optimal investment strategy. Finally, the economic implication and parameter sensitivity are analyzed by some numerical examples. We also compare the robust optimal investment strategies in two different problems.