  We develop algorithms for the numerical computation of the quadratic hedging
strategy in incomplete markets modeled by pure jump Markov process. Using the
Hamilton-Jacobi-Bellman approach, the value function of the quadratic hedging
problem can be related to a triangular system of parabolic partial
integro-differential equations (PIDE), which can be shown to possess unique
smooth solutions in our setting. The first equation is non-linear, but does not
depend on the pay-off of the option to hedge (the pure investment problem),
while the other two equations are linear. We propose convergent finite
difference schemes for the numerical solution of these PIDEs and illustrate our
results with an application to electricity markets, where time-inhomogeneous
pure jump Markov processes appear in a natural manner.

Risk Management;Pricing of Securities