Optimal time-consistent investment and reinsurance strategies for insurers under Heston's SV model

摘要

This paper considers the optimal time-consistent investment and reinsurance strategies for an insurer under Heston's stochastic volatility (SV) model. Such an SV model applied to insurers' portfolio problems has not yet been discussed as far as we know. The surplus process of the insurer is approximated by a Brownian motion with drift. The financial market consists of one risk-free asset and one risky asset whose price process satisfies Heston's SV model. Firstly, a general problem is formulated and a verification theorem is provided. Secondly, the closed-form expressions of the optimal strategies and the optimal value functions for the mean-variance problem without precommitment are derived under two cases: one is the investment-reinsurance case and the other is the investment-only case. Thirdly, economic implications and numerical sensitivity analysis are presented for our results. Finally, some interesting phenomena are found and discussed.