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DOI: 10.23952/jnfa.2026.26
Received May 19, 2026; Accepted September 12, 2026; Published October 12, 2026
Abstract. This paper solves an optimal reinsurance-investment problem for insurers under partial information with Hawkes-driven claim clustering. Since the true risk intensity is unobservable, a Gamma projection filter is used to estimate its conditional distribution. Methodologically, Malliavin calculus is introduced to derive a stochastic Hamilton-Jacobi-Bellman (HJB) equation that directly handles the non-Markovianity induced by partial-information filtering. This extends classical verification theory to non-Markovian settings. A verification theorem is established, linking smooth solutions of the stochastic HJB equation to optimal admissible strategies. Numerical experiments validate our theoretical results.
How to Cite this Article:
C. Liu, M. Liu, J. Zhang, Solving stochastic optimal control via the mutual excitation Malliavin calculus method and its applications in insurance, J. Nonlinear Funct. Anal. 2026 (2026) 26.