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Study of the risk-adjusted pricing methodology model with methods of geometrical analysis
Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab). (Financial Mathematics)
2011 (engelsk)Inngår i: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 83, nr 4-6, s. 333-345Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM) incorporates both transaction costs and the risk from a volatile portfolio. Using the Lie group analysis we obtain the Lie algebra admitted by the RAPM equation. It gives us the possibility to describe an optimal system of subalgebras and the corresponding set of invariant solutions to the model. In this way we can describe the complete set of possible reductions of the nonlinear RAPM model. Reductions are given in the form of different second order ordinary differential equations. In all cases we provide exact solutions to these equations in an explicit or parametric form. Each of these solutions contains a reasonable set of parameters which allows one to approximate a wide class of boundary conditions. We discuss the properties of these reductions and the corresponding invariant solutions.

sted, utgiver, år, opplag, sider
Abingdon: Taylor & Francis, 2011. Vol. 83, nr 4-6, s. 333-345
Emneord [en]
Transaction costs, Invariant reductions, Exact solutions, Singular perturbation
HSV kategori
Identifikatorer
URN: urn:nbn:se:hh:diva-5535DOI: 10.1080/17442508.2010.489642ISI: 000299732200003Scopus ID: 2-s2.0-84859308758OAI: oai:DiVA.org:hh-5535DiVA, id: diva2:346568
Merknad

Special Issue: Optimal stopping with Applications

Tilgjengelig fra: 2010-09-20 Laget: 2010-09-01 Sist oppdatert: 2018-03-23bibliografisk kontrollert

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