Optimal deterministic reinsurance and investment for an insurer under mean–variance criterion

This article is devoted to the study of a mean–variance problem for an insurer with deterministic reinsurance and investment strategy. The surplus process of the insurer and the financial risky asset process are described by general jump diffusion processes with random parameters. We use Malliavin calculus to obtain sufficient and necessary conditions for optimal strategy to satisfy. A particular case is discussed in which explicit expressions for optimal strategy can be derived.