Deterministic Criteria for the Absence of Arbitrage in Diffusion Models
نویسندگان
چکیده
We obtain a deterministic characterisation of the no free lunch with vanishing risk, the no generalised arbitrage and the no relative arbitrage conditions in the one-dimensional diffusion setting and examine how these notions of no-arbitrage relate to each other.
منابع مشابه
On the Martingale Property of Certain Local Martingales: Criteria and Applications
The stochastic exponential Zt = exp{Mt − M0 − (1/2)〈M,M〉t} of a continuous local martingale M is itself a continuous local martingale. We give a necessary and sufficient condition for the process Z to be a true martingale in the case where Mt = R t 0 b(Yu) dWu and Y is a one-dimensional diffusion driven by a Brownian motion W . Furthermore, we provide a necessary and sufficient condition for Z ...
متن کاملWell-posedness and invariant measures for HJM models with deterministic volatility and Lévy noise
We give sufficient conditions for existence, uniqueness and ergodicity of invariant measures for Musiela’s stochastic partial differential equation with deterministic volatility and a Hilbert space valued driving Lévy noise. Conditions for the absence of arbitrage and for the existence of mild solutions are also discussed.
متن کاملNo-arbitrage criteria for financial markets with transaction costs and incomplete information
This note deals with criteria of absence of arbitrage opportunities for an investor acting in a market with friction and having a limited access to the information flow. We develop a mathematical scheme covering major models of financial markets with transaction costs and prove several results including a criterion for the robust no-arbitrage property and a hedging theorem.
متن کاملAsymptotic arbitrage and numéraire portfolios in large financial markets
This paper deals with the notion of a large financial market and the concepts of asymptotic arbitrage and strong asymptotic arbitrage (both of the first kind), introduced in [13], [14]. We show that the arbitrage properties of a large market are completely determined by the asymptotic behavior of the sequence of the numéraire portfolios, related to small markets. The obtained criteria can be ex...
متن کاملOn arbitrage and Markovian short rates in fractional bond markets
One of the interesting problems in financial mathematics is the developing of stochastic theory of interest rates and related bond market models. The general methodology for studying term structures of interest rates proposed by Heath, Jarrow and Morton [13] was based on the investigation of a model with forward rates driven by a multi-dimensional Wiener process. This model was extended by Björ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009