From Discrete‐ to Continuous‐Time Finance: Weak Convergence of the Financial Gain Process1
- 1 January 1992
- journal article
- Published by Wiley in Mathematical Finance
- Vol. 2 (1) , 1-15
- https://doi.org/10.1111/j.1467-9965.1992.tb00022.x
Abstract
Conditions suitable for applications in finance are given for the weak convergence (or convergence in probability) of stochastic integrals. For example, consider a sequence Sn of security price processes converging in distribution to S and a sequence θn of trading strategies converging in distribution to θ. We survey conditions under which the financial gain process θn dSn converges in distribution to θ dS. Examples include convergence from discrete‐ to continuous‐time settings and, in particular, generalizations of the convergence of binomial option replication models to the Black‐Scholes model. Counterexamples are also provided.Keywords
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