2020/10/23 by Xia Han, Han, Xia, Zhibin Liang +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #FOS: Economics and business #FOS: Mathematics #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Probability and Risk Models
paper · pdf · doi:10.48550/arxiv.2010.12158
openalex publication_date 2020/10/23 · openalex created_date 2020/10/29 · openalex updated_date 2026/07/28
In this paper, we study an optimal reinsurance-investment problem in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. We assume that the insurer can purchase per-loss reinsurance for each line of business and invest its surplus in a financial market consisting of a risk-free asset and a risky asset. Under the criterion of minimizing the probability of drawdown, the closed-form expressions of the optimal reinsurance-investment strategy and the corresponding value function are obtained. We show that the optimal reinsurance strategy is in the form of pure excess-of-loss reinsurance strategy under the expected value principle, and under the variance premium principle, the optimal reinsurance strategy is in the form of pure quota-share reinsurance. Furthermore, we extend our model to the case where the insurance company involves n (n≥3) dependent classes of insurance business and the optimal results are derived explicitly as well.