Related papers: On the Existence of Consistent Price Systems
Under proportional transaction costs, a price process is said to have a consistent price system, if there is a semimartingale with an equivalent martingale measure that evolves within the bid-ask spread. We show that a continuous,…
In markets with transaction costs, consistent price systems play the same role as martingale measures in frictionless markets. We prove that if a continuous price process has conditional full support, then it admits consistent price systems…
We use the machinery of a conditional probability space (R\'enyi, 1955) to obtain an Agreement Theorem (Aumann, 1976) under general conditions. A conditional probability space (CPS) is a family of probability measures defined relative to a…
We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Through several applications we show how the condition…
A relatively complete picture on the steady states of the following Schr$\ddot{o}$dinger-Poisson-Slater (SPS) system \[ \begin{cases} -\Delta Q+Q=VQ-C_{S}Q^{2}, & Q>0\text{ in }\mathbb{R}^{3}\\ Q(x)\to0, & \mbox{as }x\to\infty,\\ -\Delta…
Stability Selection was recently introduced by Meinshausen and Buhlmann (2010) as a very general technique designed to improve the performance of a variable selection algorithm. It is based on aggregating the results of applying a selection…
In this note, we study the infinite-dimensional conditional laws of Brownian semistationary processes. Motivated by the fact that these processes are typically not semimartingales, we present sufficient conditions ensuring that a Brownian…
The COS method proposed in Fang and Oosterlee (2008), although highly efficient, may lack robustness for a number of cases. In this paper, we present a Stable pricing of call options based on Fourier cosine series expansion. The Stability…
This paper explores conditions of existence of different types of consistent tests. New links of these types of consistency are also established. The existence of discernible (strong consistent) tests follows from the existence of pointwise…
It has been challenging for the technical and regulatory communities to formulate requirements for trustworthiness of the cyber-physical systems (CPS) due to the complexity of the issues associated with their design, deployment, and…
This paper introduces a formal definition of a Cyber-Physical System (CPS) in the spirit of the CPS Framework proposed by the National Institute of Standards and Technology (NIST). It shows that using this definition, various problems…
We study the satisfiability of ordering constraint satisfaction problems (CSPs) above average. We prove the conjecture of Gutin, van Iersel, Mnich, and Yeo that the satisfiability above average of ordering CSPs of arity $k$ is…
Under the same assumptions made by Mas-Colell et al. (1995), I develop a short, simple, and complete proof of existence of equilibrium prices based on excess demand functions. The result is obtained by applying the Brouwer fixed point…
Cyber-physical systems (CPS) are assemblies of networked, heterogeneous, hardware, and software components sensing, evaluating, and actuating a physical environment. This heterogeneity induces complexity that makes CPSs challenging to model…
This paper introduces a novel framework for analysing equilibrium in structured production systems incorporating a static social division of labour by distinguishing between consumption goods traded in competitive markets and intermediate…
We consider the class of valuations on indivisible items called gross-substitute (GS). This class was introduced by Kelso and Crawford (1982) and is widely used in studies of markets with indivisibilities. GS is a condition on the…
The development of cyber-physical system (CPS) is a big challenge because of its complexity and its complex requirements. Especially in Requirements Engineering (RE), there exist many redundant and conflict requirements. Eliminating…
This paper presents the general form and essential properties of the q-optimal measure following the approach of Delbaen and Schachermayer (1996) and proves its existence under mild conditions. Most importantly, it states a necessary and…
In discrete time markets with proportional transaction costs, Schachermayer (2004) shows that robust no-arbitrage is equivalent to the existence of a strictly consistent price system. In this paper, we introduce the concept of prospective…
This paper is intended to review recent results and open problems concerning the existence of steady states to the Maxwell-Schr\"odinger system. A combination of tools, proofs and results are presented in the framework of the…