Abstract
This paper considers a robust optimal reinsurance-investment problem for an insurer with mispricing and model ambiguity. The surplus process is described by a classical Cramér-Lunderg model and the financial market contains a market index, a risk-free asset and a pair of mispriced stocks, where the expected return rate of the stocks and the mispricing follow mean reverting processes which take into account liquidity constraints. In particular, both the insurance and reinsurance premium are assumed to be calculated via the variance premium principle. By employing the dynamic programming approach, we derive the explicit optimal robust reinsurance-investment strategy and the optimal value function.
Highlights
Reinsurance and investment are the main tools for insurers to manage the risk and profit
This paper considers a robust optimal reinsurance-investment problem for an insurer with mispricing and model ambiguity
The surplus process is described by a classical Cramér-Lunderg model and the financial market contains a market index, a risk-free asset and a pair of mispriced stocks, where the expected return rate of the stocks and the mispricing follow mean reverting processes which take into account liquidity constraints
Summary
Reinsurance and investment are the main tools for insurers to manage the risk and profit. Gu et al [16] discuss optimal proportional reinsurance-investment problem for an insurer with mispricing and model ambiguity. We seek the optimal proportional reinsurance-investment problem with mispricing under observed mean-reverting stochastic risk premium. Zeng et al [17] and Gu et al [18] investigate the optimal proportional reinsurance-investment problem for an insurer with mispricing, model ambiguity with mean-reversion under expected value premium principle. Motivated by these papers, both the insurance and reinsurance premium payments are calculated by using the variance premium principle in this paper.
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