Lévy processes

Svetlana Boyarchenko and Sergei Z. Levendorskiĭ
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Sergei Z. Levendorskiĭ: Rostov State University of Economics, Russia

Chapter 2 in Non-Gaussian Merton-Black-Scholes Theory, 2002, pp 39-66 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractThe following sections are included:Basic notation and definitionsRandom variablesConditional expectationThe Fourier transform and the Laplace transform. Characteristic functionsLévy processes: general definitionsLévy processes and infinitely divisible distributionsThe Lévy-Khintchine formula and generating tripletConstructions of Lévy processesExplicit constructionsSubordinators and subordinated processesLinear transformations of Lévy processesThe Wiener-Hopf factorizationLévy processes as Markov processesMarkov property and Feller propertyStopping times and the strong Markov propertyResolvent operator and infinitesimal generatorDynkin's formulaDualityAbsolutely continuous resolventsOperators $P^q_B$Boundary value problems for the Black-Scholes-type equationBoundary problems for the stationary Black-Scholes type equationBoundary problems for the non-stationary Black-Scholes type equationCommentary

Keywords: Non-Gaussian Models; Merton-Black-Scholes Theory; Levy Processes; American Options; European Options; Feller Processes (search for similar items in EconPapers)
Date: 2002
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