Let Q be the set of equivalent martingale measures for a given process S, and let X be a process which is a local supermartingale with respect to any measure in Q. The optional decomposition theorem for X states that there exists a predictable integrand ф such that the difference X−ф•S is...

In the high-frequency limit, conditional expected increments of fractional Brownian motion converge to a white noise, shedding their dependence on the path history and the forecasting horizon, and making dynamic optimization problems tractable. We find an explicit formula for locally...

We investigate the term structure for the case when interest rates are allowed to be driven by a general marked point process as well as by a Wiener process. Developing a theory which allows for measure-valued trading portfolios we study existence and uniqueness of a martingale measure, as well...

Let Q be the set of equivalent martingale measures for a given process S, and let X be a process which is a local supermartingale with respect to any measure in Q. The optional decomposition theorem for X states that there exists a predictable integrand ф such that the difference X−ф•S is...

Let Q be the set of equivalent martingale measures for a given process S, and let X be a process which is a local supermartingale with respect to any measure in Q. The optional decomposition theorem for X states that there exists a predictable integrand ф such that the difference X−ф•S is...

Written on the occasion of the centenary of Louis Bachelier's 1900 PhD thesis “Théorie de la spéculation”, this paper puts Bachelier into a historical perspective. It explains his role as a pioneer in both mathematical finance and probability theory, and it also gives a careful account of...

The paper deals with definition of supremal sets in a rather general framework where deterministic and random preference relations (preorders) and partial orders are defined by continuous multi-utility representations. It gives a short survey of the approach developed in [4], [5] with some new...

In the first part of the paper we study concepts of supremum and maximum as subsets of a topological space X endowed by preference relations. Several rather general existence theorems are obtained for the case where the preferences are defined by countable semicontinuous multi-utility...

Inspired by the theory of financial markets with transaction costs, we study a concept of essential supremum in the framework where a random partial order in $\R^d$ is lifted to the space $L^0(\R^d)$ of $d$-dimensional random variables. In contrast to the classical definition, we define the...