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We give an elementary proof of the celebrated Bichteler-Dellacherie Theorem which states that the class of stochastic processes $S$ allowing for a useful integration theory consists precisely of thos...
Based on a criterium of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Dep...
We obtain a deterministic characterisation of the \emph{no free lunch with vanishing risk}, the \emph{no generalised arbitrage} and the \emph{no relative arbitrage} conditions in the one-dimensional d...
We generalize Merton's asset valuation approach to systems of multiple financial firms where cross-ownership of equities and liabilities is present. The liabilities, which may include debts and deriva...
Hedging under arbitrage     Hedging  arbitrage       2010/10/19
It is shown that delta hedging provides the optimal trading strategy in terms of minimal required initial capital to replicate a given terminal payoff in a continuous-time Markovian context. This hol...
In 1999 Robert Fernholz observed an inconsistency between the normative assumption of existence of an equivalent martingale measure (EMM) and the empirical reality of diversity in equity markets. We ...
Arbitrage strategy     Arbitrage strategy  profit  financial instruments       2010/10/18
An arbitrage strategy allows a financial agent to make certain profit out of nothing, i.e., out of zero initial investment. This has to be disallowed on economic basis if the market is in equilibrium ...
Consider a frictionless market trading a finite number of co-maturing European call and put options written on a risky asset plus an instrument with path-dependent payoff known as a weighted variance...
We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to.
In a semimartingale financial market model, it is shown that there is equivalence be-tween absence of arbitrage of the first kind (a weak viability condition) and the existence of a strictly positive ...
The recent ‘correlation breakdown’ in the modeling of credit default swaps,in which model correlations had to exceed 100% in order to reproduce market prices of supersenior tranches, is analyzed and a...
In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models driven by fractional Brownian motions. By using support arguments we prove that the resulting model is arbitrage free under pro...
In nonlinear pricing environment with correlated types, we characterize optimal selling mechanisms when buyers could form a coalition to coordinate their reports and to arbitrage on the goods. We find...
Strict local martingales may admit arbitrage opportunities with respect to the class of simple trading strategies. (Since there is no possibility of using doubling strategies in this framework, the lo...
The law of large numbers introduces an order of where N is the number of elements in a linear stochastic system with or without growth. Comparing observed magnitudes of macro fluctuations and numbers ...

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