2013/05/17 by Jacek Jakubowski, Jakubowski, Jacek, Mariusz Niewęgłowski +2
Economics, Econometrics and Finance · Social Sciences · #60H30 #91G80 #FOS: Economics and business #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Pricing of Securities (q-fin.PR) #Primary 91G40 #Secondary 91G20 #Stochastic processes and financial applications #msc:60H30 #msc:91G20 #msc:91G40 #msc:91G80 #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1305.4132
openalex publication_date 2013/05/17 · arxiv created 2013/07/24 · arxiv updated 2013/07/25 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
At first, we solve a problem of finding a risk-minimizing hedging strategy on a general market with ratings. Next, we find a solution to this problem on Markovian market with ratings on which prices are influenced by additional factors and rating, and behavior of this system is described by SDE driven by Wiener process and compensated Poisson random measure and claims depend on rating. To find a tool to calculate hedging strategy we prove a Feynman-Kac type theorem. This result is of independent interest and has many applications, since it enables to calculate some conditional expectations using related PIDE's. We illustrate our theory on two examples of market. The first is a general exponential Lévy model with stochastic volatility, and the second is a generalization of exponential Lévy model with regime-switching.