Abstract. The present paper provides a continuous-time Markov chain (CTMC) model approach to financial markets. Sufficient conditions which guarantee the absence of arbitrage and the completeness of rather generic market models, aro also derived.

Then, by proving a weak converge result, we show that the CTMC model can be viewed as a generalization of the geometric Poisson model, the Black-Scholes model and the Merton model.

Received: September 6, 2016

Revised: October 5, 2016

Published: October 9, 2016

AMS Subject Classification: 60H15, 60H35, 91B60, 91G20, 91G60

Key Words and Phrases: continuous-time Markov chain, geometric Brownian motion, compound Poisson process, geometric Poisson process, weak convergence, market modeling, finance
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DOI: 10.12732/ijpam.v109i4.21 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 4
Pages: 1029 - 1054

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This work is licensed under the Creative Commons Attribution International License (CC BY).

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