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At first, we solve a problem of finding a risk-minimizing hedging strategy ona general market with ratings. Next, we find a solution to this problem onMarkovian market with ratings on which prices are influenced by additionalfactors and rating, and behavior of this system is described by SDE driven byWiener process and compensated Poisson random measure and claims depend onrating. To find a tool to calculate hedging strategy we prove a Feynman-Kactype theorem. This result is of independent interest and has many applications,since it enables to calculate some conditional expectations using relatedPIDE's. We illustrate our theory on two examples of market. The first is ageneral exponential L\'{e}vy model with stochastic volatility, and the secondis a generalization of exponential L\'{e}vy model with regime-switching.

Risk-minimization and hedging claims on a jump-diffusion market model, Feynman-Kac Theorem and PIDE