Valuation and dynamic replication of contingent claims in the framework of the beliefs-preferences gauge symmetry
Research Group, TXU Energy Trading, 1717 Main Street,
Dallas, TX 75201, USA
Corresponding author: a firstname.lastname@example.org
Published online: 15 May 2002
Although symmetries play a major role in physics, their use in finance is relatively new and, to the best of our knowledge, can be traced to 1995 when Kholodnyi introduced the beliefs-preferences gauge symmetry. One of the main outcomes of the beliefs-preferences gauge symmetry is that it allows for the valuation and dynamic replication of contingent claims in a general market environment, that is, in the case of a general, not necessarily diffusion Markov process for the prices of underlying securities. This valuation and dynamic replication is based on the novel ideas of symmetry in contrast to the standard approach which uses stochastic analysis. The practical applications of the beliefs-preferences gauge symmetry range from the detection of a new type of true arbitrage to the beliefs-preferences-independent valuation and dynamic replication of contingent claims in a general market environment.
PACS: 11.15.-q – Gauge field theories / 02.40.-k – Geometry, differential geometry, and topology / 02.20.-a – Group theory / 02.50.-r – Probability theory, stochastic processes, and statistics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002