The course aims to provide an introduction to computational methods in Finance and Insurance. In particular, at the end of the course students will be able to solve various relevant problems in Actuarial and Financial Sciences. Computer simulations of practical test cases will be implemented with the aid of Matlab.

• brief introduction/review of: stochastic differential equations, Black-Scholes model, jump-diffusion processes, ruin probability
• the Monte Carlo method: advantages and disadvantages; variance reduction techniques
• the finite difference method: stability, consistency and convergence
• binomial/trinomial trees for option pricing; implementation and convergence issues
• entually: the finite element method
• Matlab applications (Black-Scholes, exotic options, ruin probability)

Financial mathematics (advanced), Probability and Stochastic Processes