Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 62, pp. 1-10.

Title:  Solutions to  integro-differential parabolic problems
        arising in the pricing of financial options in a Levy market

Authors:  Ionut Florescu  (Stevens Institute of Tech., Hoboken, NJ, USA)
          Maria Cristina Mariani (The Univ. of Texas at El Paso, TX, USA)

Abstract:
 We study an integro-differential parabolic problem modelling
 a process with jumps and stochastic volatility in financial
 mathematics. Under suitable conditions, we prove the existence
 of solutions in a general domain using the method of upper
 and lower solutions and a diagonal argument.

Submitted September 10, 2009. Published May 05, 2010.
Math Subject Classifications: 35K99, 45K05, 91680.
Key Words: Integro-differential parabolic equations; financial mathematics,
           Levy markets; jumps processes; stochastic volatility