This PhD thesis aims to study financial processes which have semi-heavy-tailed marginal distributions and may exhibit memory. The traditional Black-Scholes model is expanded to incorporate memory via an integral operator, resulting in a class of market models which still preserve the...

Guasoni (2006) introduced a simple condition for the absence of arbitrage opportunities. In this note we show that his results remain valid under a weaker notion of arbitrage which arises by excluding liquidation costs from the value process of a portfolio.

This thesis will first criticize standard financial theory. The focus will be on return distributions, efficient market hypothesis and the independence of returns. Part two gives the intuition to look at markets in a different view. Namely the one proposed by B. Mandelbrot who has shown that...

We present general conditions for the weak convergence of a discrete-time additive scheme to a stochastic process with memory in the space D [ 0,T ]. Then we investigate the convergence of the related multiplicative scheme to a process that can be interpreted as an asset price with memory. As an...

A major application of rescaled adjusted range analysis (RS analysis) is the study of price fluctuations in financial markets. There, the value of the Hurst constant, H, in a time series may be interpreted as an indicator of the irregularity of the price of a commodity, currency or similar...