Research On Optimal Investment-Reinsurance Problem Under Model Uncertainty

The field of insurance mathematics is a very natural and very importan-t field of application of stochastic control theory.An insurer can reduce risk and improve return through reinsurance and investment.How to choose the best business strategy to achieve established business goals is a problem that the insurer must consider.At present,most literature studied the investment-reinsurance problem under variance premium principle or mean variance cri-terion with various restrictions such as non-short selling,transaction fees and terminal constraint.Dynamic programming principle was used to give a strate-gic solution to the problem.In fact,due to the impact of global financial crisis and European debt crisis,there are many uncertainties in financial market and insurance industry.It is of certain practical significance to study some optimal investment-reinsurance problems under model uncertainty.At the same time,the insurer has some business objectives.Research on investment-reinsurance problems with state constraints and jump diffusion risk process is closer to reality.Therefore,the main research results of this paper are as follows:(1)We study an optimal investment-reinsurance problem of the insurer where foreign exchange investment,consumption and proportional reinsurance are considered under model uncertainty.First,we transform the problem in-to a two-person zero-sum stochastic differential game driven by the forward-backward stochastic differential equation by introducing a family of probability measures.Then,we use the stochastic maximum principle to obtain the op-timal investment-reinsurance strategy,and give an explicit expression of the optimal strategy solution in a specific situation.(2)We study an optimal investment-reinsurance problem of the insurer with state constraint and jump diffusion risk process under model uncertainty,where the price of foreign exchange risk assets obeys the jump diffusion risk process.First,we establish the stochastic maximum principle of the forward-backward stochastic control system with jump diffusion risk process and s-tate constraint by virtue of Clarke generalized derivative,Ekeland's variational principle and the convex variation method.Then,we obtain an optimal pol-icy solution of the insurer.In special cases,the dual method and the direct construction method are used to give the explicit optimal policy solution.