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Valuation and Dynamic Replication of Contingent Claims in a General Market Environment Based on the Beliefs-Preferences Gauge Symmetry

Authors
Publisher
Elsevier B.V.
Publication Date
Keywords
  • Applied Mathematics
  • Modelling And Simulation
  • Probability Theory And Stochastic Processes
  • Applied_Mathematics/0111016
Disciplines
  • Mathematics

Abstract

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.

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