Elementary stochastic calculus for finance with infinitesimals. (English) Zbl 1424.60070
Summary: The concept of an equivalent martingale measure is of key importance for pricing of financial derivative contracts. The goal of the paper is to apply infinitesimals in the non-standard analysis set-up to provide an elementary construction of the equivalent martingale measure built on hyperfinite binomial trees with infinitesimal time steps.
MSC:
| 60H05 | Stochastic integrals |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
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