Optimal investment and risk control for an insurer with partial information in an anticipating environment

Abstract

This paper considers an optimal investment and risk control problem under the criterion of logarithm utility maximization. The risky asset process and the insurance risk process are described by stochastic differential equations with jumps and anticipating coefficients. The insurer invests in the financial assets and controls the number of policies based on some partial information about the financial market and the insurance claims. The forward integral and Malliavin calculus for Lévy processes are used to obtain a characterization of the optimal strategy. Some special cases are discussed and the closed-form expressions for the optimal strategies are derived.

Keywords:

• Investment
• risk control
• partial information
• anticipating environment
• forward integrals
• Malliavin calculus

Acknowledgements

The authors are very grateful to the Editor and an anonymous referee for their helpful comments and suggestions, which led to an improvement of the presentation of the work.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Supported by the National Natural Science Foundation of China [grant numbers 11701436, 11661074] and the Fundamental Research Funds for Central Universities [grant numbers 2018IB019 and 2018IVB014].