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This work considers a stochastic model in which the uncertainty is driven by a multidimensional Brownian motion. The market price of risk process makes the transition between real world probability measure and risk neutral probability…
We introduce fractional Brownian motion processes (fBm) as an alternative model for the turbulent index of refraction. These processes allow to reconstruct most of the index properties, but they are not differentiable. We overcome the…
In this paper, we study the martingale property for a Scott correlated stochastic volatility model, when the correlation coefficient between the Brownian motion driving the volatility and the one driving the asset price process is…
Stochastic integration \textit{wrt} Gaussian processes has raised strong interest in recent years, motivated in particular by its applications in Internet traffic modeling, biomedicine and finance. The aim of this work is to define and…
Starting solely with a set of possible prices for a traded asset $S$ (in infinite discrete time) expressed in units of a numeraire, we explain how to construct a Daniell type of integral representing prices of integrable functions depending…
This paper considers a sequence of discrete-time random walk markets with a safe and a single risky investment opportunity, and gives conditions for the existence of arbitrages or free lunches with vanishing risk, of the form of waiting to…
We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of…
White noise is a fundamental and fairly well understood stochastic process that conforms the conceptual basis for many other processes, as well as for the modeling of time series. Here we push a fresh perspective toward white noise that,…
We investigate Wiener-transformable markets, where the driving process is given by an adapted transformation of a Wiener process. This includes processes with long memory, like fractional Brownian motion and related processes, and, in…
We consider a general class of diffusion-based models and show that, even in the absence of an Equivalent Local Martingale Measure, the financial market may still be viable, in the sense that strong forms of arbitrage are excluded and…
We consider a market with fractional Brownian motion with stochastic integrals generated by the Riemann sums. We found that this market is arbitrage free if admissible strategies that are using observations with an arbitrarily small delay.…
In this paper, we introduce a numeraire-free and original probability based framework for financial markets. We reformulate or characterize fair markets, the optional decomposition theorem, superhedging, attainable claims and complete…
This paper builds on our earlier proposal for construction of a positive inner product for pseudo-Hermitian Hamiltonians and we give several examples to clarify our method. We show through the example of the harmonic oscillator how our…
The purpose of this paper is two-fold. First is to extend the notions of an n-dimensional semimartingale and its stochastic integral to a piecewise semimartingale of stochastic dimension. The properties of the former carry over largely…
The Black-Litterman model is a framework for incorporating forward-looking expert views in a portfolio optimization problem. Existing work focuses almost exclusively on single-period problems with the forecast horizon matching that of the…
The stochastic parabolic equations with random potentials, driving forces and initial conditions are considered. The Wick product is used to give sense to the product of two generalized stochastic processes, and the existence and uniqueness…
We present two models for incorporating the total effect of market microstructure noise into dynamic pricing of assets and European options. The first model is developed under a Black-Scholes-Merton, continuous-time framework. The second…
We develop the fundamental theorem of asset pricing in a probability-free infinite-dimensional setup. We replace the usual assumption of a prior probability by a certain continuity property in the state variable. Probabilities enter then…
Based on empirical market data, a stochastic volatility model is proposed with volatility driven by fractional noise. The model is used to obtain a risk-neutrality option pricing formula and an option pricing equation.
We consider a generic market model with a single stock and with random volatility. We assume that there is a number of tradable options for that stock with different strike prices. The paper states the problem of finding a pricing rule that…