2015/06/30 by Anindya Goswami, Jeeten Patel, Poorva Shevgaonkar
Mathematics · Economics, Econometrics and Finance · #math.AP #math.PR #q-fin.PR #msc:60K15 #msc:91B30 #msc:91G20 #msc:91G60
paper · pdf · doi:10.1080/07362994.2016.1189340
published as Stoch. Anal. Appl. 34(2016) no. 5, 893-905 · 7 pages. arXiv admin note: substantial text overlap with arXiv:1408.5266
arxiv created 2016/05/05 · arxiv updated 2016/09/27
This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. In a semi-Markov modulated GBM model the locally risk minimizing price function satisfies a special case of this problem. We study the well-posedness of the problem via a Volterra integral equation of second kind. A probabilistic approach, in particular the method of conditioning on stopping times is used for showing uniqueness.