Electron. J. Diff. Equ., Vol. 2010(2010), No. 62, pp. 1-10.

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

Ionut Florescu, Maria Cristina Mariani

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 5, 2010.
Math Subject Classifications: 35K99, 45K05, 91680.
Key Words: Integro-differential parabolic equations; financial mathematics, Levy markets; jumps processes; stochastic volatility

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Ionut Florescu
Department of Mathematical Sciences
Stevens Institute of Technology
Castle Point on Hudson, Hoboken, NJ 07030, USA
email: Ionut.Florescu@stevens.edu
Maria Christina Mariani
Department of Mathematical Sciences
The University of Texas at El Paso
Bell Hall 124, El Paso, TX 79968-0514, USA
email: mcmariani@utep.edu

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