Optimal Investment-reinsurance Policy With Regime Switching And Value-at-risk Constraint

As the large enterprises,the insurance companies make profits by selling policies and investing in financial markets.Therefore,they face various risks,such as claims risk and market risk,which can lead to bankruptcy if the risk is too large.How to control risks becomes an important issue in the asset management of insurance companies.In the past decade,the investment and reinsurance model has become one of the popular models for related problems.The insurance companies can investment in the finance market to increase the its asset,and reduce the risk by purchasing the reinsurance contract.This paper consider the optimal investment-reinsurance problem for an insurance company which is subject to a dynamic Value-at-Risk(VaR)constraint in a Markovian regime-switching environment.Its goal is minimizing the ruin probability.The Markovian process is introduced to simulate the market state,and the VaR constraint is used by us to control the possible loss.We establish an optimal control model to describe this problem.The coupled HJB equations are derived using the dynamic programming principle and the Lagrangian multiplier method is used to deal with the VaR constraints.We offer a numerical method to solve the above-mentioned HJB equations with constraints.A practical example is used to verify the validity of the method.Finally,we give the following conclusions:(1)The VaR constraint will impose a constant upper bound on the investment and reinsurance st.rategy in both regimes.In the high regime,the constraints are stronger;(2)In the high regime,the insurance companies with less wealth will show a fear of the bad market status,and tend to adopt more risky strategies.(3)Even if the VaR constraint is very effective on the optimal strategy,the effect on ruin probability is also very small.