Statistics Seminars: Absence of Arbitrage in a General Framework
2 December 2013 14:00 in CM221
It is well known that fractional Brownian motion admits arbitrage within the class of admissible continuous trading strategies. It was shown that arbitrage possibilities can be excluded by suitably restricting the class of allowable trading strategies in fi?nancial markets that
consist of a money market account and a risky asset. In this note, we show an analogous result in a multi-asset market where the discounted risky asset
prices follow more general non-semimartingale models. In our framework, investors are allowed
to trade between a risk-free asset and multiple risky assets by following simple trading strategies
that require a minimal deterministic waiting time between any two trading dates. We present a
condition on the discounted risky asset prices that guarantee absence of arbitrage in this setting.
We give examples that satisfy our condition and study its invariance under certain transformations.
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