2012/06/23 by Carmine De Franco, Peter Tankov, De Franco, Carmine +3
Decision Sciences · Economics, Econometrics and Finance · Engineering · #91G60 #91G80 #Economic theories and models #Electric Power System Optimization #FOS: Economics and business #Pricing of Securities (q-fin.PR) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Stochastic processes and financial applications #msc:91G60 #msc:91G80 #q-fin.PR #q-fin.RM
paper · pdf · doi:10.48550/arxiv.1206.5393
37 pages
openalex publication_date 2012/06/23 · arxiv created 2013/12/11 · arxiv updated 2013/12/12 · openalex created_date 2022/08/22 · openalex updated_date 2026/07/28
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.