Under inflation influence

an optimal time-consistent strategy selection problem for claims dependent risk model is studied. The two claim number processes are correlated by a common Poisson process. The insurer can purchase reinsurance for reducing claims and invest its surplus in finance market for increasing wealth. In the process of investment

the effect of inflation is taken into account

and the effect of inflation is achieved through the conversion of the risk asset to the inflation rate. The objective of the insurer is to choose an optimal time-consistent reinsurance-investment strategy so as to maximize the expected terminal surplus while minimizing the variance of the terminal surplus. Since this problem is time-inconsistent

it is studied by placing the problem within a game theoretic framework. Applying Hamilton-Jacobi-Bellman dynamic programming approach

closed form solutions for the optimal reinsurance-investment strategy and the corresponding value functions are obtained. Finally

the influence of some insurance market model parameters on optimal reinsurance strategy is explained by numerical calculation

and the influence of financial market model parameters and inflation model parameters on optimal investment strategy are also given. Through this study

it can guide investors to make reasonable investment under the influence of inflation

so that their wealth is the largest and the smallest risk.