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Principles of financial product synthesis from a few basic financial products constitute an interesting research topic inspired by Islamic finance. We make an effort to answer general questions that should be answered before starting to…
Many financial and economic variables, including financial returns, exhibit nonlinear dependence, heterogeneity and heavy-tailedness. These properties may make problematic the analysis of (non-)efficiency and volatility clustering in…
Predictions are the currency of a machine learning model, and to understand the model's behavior over segments of a dataset, or over time, is an important problem in machine learning research and practice. There currently is no systematic…
The financial market is nonpredictable, as according to the Bachelier, the mathematical expectation of the speculator is zero. Nevertheless, we observe in the price fluctuations the two distinct scales, short and long time. Behaviour of a…
An analysis of the stylized facts in financial time series is carried out. We find that, instead of the heavy tails in asset return distributions, the slow decay behaviour in autocorrelation functions of absolute returns is actually…
Establishing the emergence of evolutionary behavior as a defining characteristic of 'life' is a major step in the Artificial life (ALife) studies. We present here an abstract formal framework for this aim based upon the notion of high-level…
We establish new results for estimation and inference in financial durations models, where events are observed over a given time span, such as a trading day, or a week. For the classical autoregressive conditional duration (ACD) models by…
In this paper we shall prove that the plane of financial events, introduced and applied to financial problems by the author himself (see [2], [3] and [4]) can be considered as a fibration in two different ways. The first one, the natural…
We introduce, in continuous time, an axiomatic approach to assign to any financial position a dynamic ask (resp. bid) price process. Taking into account both transaction costs and liquidity risk this leads to the convexity (resp. concavity)…
The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…
Process algebra and temporal logic are two popular paradigms for the specification, verification and systematic development of reactive and concurrent systems. These two approaches take different standpoint for looking at specifications and…
Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking…
Qualitative spatial and temporal reasoning is based on so-called qualitative calculi. Algebraic properties of these calculi have several implications on reasoning algorithms. But what exactly is a qualitative calculus? And to which extent…
In the present paper a model of a market consisting of real and financial interacting sectors is studied. Agents populating the stock market are assumed to be not able to observe the true underlying fundamental, and their beliefs are biased…
Dynamic graphs serve as a generic abstraction and description of the evolutionary behaviors of various complex systems (e.g., social networks and communication networks). Temporal link prediction (TLP) is a classic yet challenging inference…
This paper motivates the need for a formalism for the modelling and analysis of dynamic reconfiguration of dependable real-time systems. We present requirements that the formalism must meet, and use these to evaluate well established…
We consider the valuation of contingent claims with delayed dynamics in a Black&Scholes complete market model. We find a pricing formula that can be decomposed into terms reflecting the market values of the past and the present, showing how…
Expectiles are statistical parameters which also provide a class of sublinear risk measures in finance. They are solutions of continuous optimization problems. The corresponding first order condition provides two different fixed point…
We consider a general discrete-time financial market with proportional transaction costs as in [Kabanov, Stricker and R\'{a}sonyi Finance and Stochastics 7 (2003) 403--411] and [Schachermayer Math. Finance 14 (2004) 19--48]. In addition to…
Mathematical models with time dependent parameters are of great interest in financial Mathematics because they capture real life scenarios in the financial market. In this study, via the Lie group technique, we analyse evolution-type…