As Non-Life Insurance models are strictly connected with stochastic processes, the main aim of this book is to show how classical and recent advanced stochastic models can be used to improve the stochastic approach in non-life insurance for which contracts can be characterized by time and risk: this constitutes precisely the core business of stochastic processes. This book presents various stochastic methods applied to non-life insurance, in order to price, valuate, hedge and manage these contracts and particularly to model the various claim processes.

From the financial point of view, essential concepts such as actuarial evaluation, market values, fair pricing play a central role and will be presented. For the insurance part, the age assumes a fundamental role in the evaluation of premiums; this influence should be function not only of the age of insured but also, for example in car insurance, of the age of car.

For these processes, we develop fundamental applications for non-life insurance such claim management, reinsurance, catastrophic risks, car insurance and the application in the actuarial risk theory particularly for the computing of main risk and Solvency II indicators such as the SCR and MCR indicators. We include numerical applications and practical case studies.