Differential and Integral Equations

Nonlinear integro-differential evolution problems arising in option pricing: a viscosity solutions approach

Anna Lisa Amadori

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Abstract

A class of nonlinear integro-differential Cauchy problems is studied by means of the viscosity solutions approach. In view of financial applications, we are interested in continuous initial data with exponential growth at infinity. Existence and uniqueness of solution is obtained through Perron's method, via a comparison principle; besides, a first order regularity result is given. This extension of the standard theory of viscosity solutions allows to price derivatives in jump--diffusion markets with correlated assets, even in the presence of a large investor, by means of the PDE's approach. In particular, derivatives may be perfectly hedged in a completed market.

Article information

Source
Differential Integral Equations, Volume 16, Number 7 (2003), 787-811.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060597

Mathematical Reviews number (MathSciNet)
MR1988725

Zentralblatt MATH identifier
1052.35083

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35R10: Partial functional-differential equations 60J75: Jump processes 91B24: Price theory and market structure 91B26: Market models (auctions, bargaining, bidding, selling, etc.)

Citation

Amadori, Anna Lisa. Nonlinear integro-differential evolution problems arising in option pricing: a viscosity solutions approach. Differential Integral Equations 16 (2003), no. 7, 787--811. https://projecteuclid.org/euclid.die/1356060597


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