The article introduces a new method for pricing and managing financial risks using a special type of risk measure called g_\Gamma-solution. This method is different from the usual market-based approach and offers a more general way to handle risks in various situations. By applying the inf-convolution of convex risk measures, the researchers were able to solve optimization problems effectively. The use of g_\Gamma-solution led to the development of dynamic risk measures and provided insights into optimal decision-making processes in finance.