Related papers: No-Free-Lunch equivalences for exponential Levy mo…
We propose a continuous time model for financial markets with proportional transactions costs and a continuum of risky assets. This is motivated by bond markets in which the continuum of assets corresponds to the continuum of possible…
We study the existence of the numeraire portfolio under predictable convex constraints in a general semimartingale model of a financial market. The numeraire portfolio generates a wealth process, with respect to which the relative wealth…
The concept of absence of opportunities for free lunches is one of the pillars in the economic theory of financial markets. This natural assumption has proved very fruitful and has lead to great mathematical, as well as economical, insights…
The hypothesis that there do not exist free lunches with vanishing risk (FLVRs) in the real market underpins the popular risk-neutral pricing and hedging methodology in quantitative finance. The paper documents the fact that this hypothesis…
We propose a unified analysis of a whole spectrum of no-arbitrage conditions for financial market models based on continuous semimartingales. In particular, we focus on no-arbitrage conditions weaker than the classical notions of No…
The main result of the paper is a version of the fundamental theorem of asset pricing (FTAP) for large financial markets based on an asymptotic concept of no market free lunch for monotone concave preferences. The proof uses methods from…
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…
Under short sales prohibitions, no free lunch with vanishing risk (NFLVR-S) is known to be equivalent to the existence of an equivalent supermartingale measure for the price processes (Pulido [22]). For two given price processes, we…
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…
We show that the existence of an equivalent local martingale measure for asset prices does not prevent negative prices for European calls written on positive stock prices. In particular, we illustrate that many standard no-arbitrage…
This paper is concerned with learners who aim to learn patterns in infinite binary sequences: shown longer and longer initial segments of a binary sequence, they either attempt to predict whether the next bit will be a 0 or will be a 1 or…
We consider a global market constituted by several submarkets, each with its own assets and num\'eraire. We provide theoretical foundations for the existence of equivalent martingale measures and results on superreplication prices which…
In the context of large financial markets we formulate the notion of \emph{no asymptotic free lunch with vanishing risk} (NAFLVR), under which we can prove a version of the fundamental theorem of asset pricing (FTAP) in markets with an…
Tensor network machine learning models have shown remarkable versatility in tackling complex data-driven tasks, ranging from quantum many-body problems to classical pattern recognitions. Despite their promising performance, a comprehensive…
The present article provides a novel theoretical way to evaluate tradeability in markets of ordinary exponential L\'evy type. We consider non-tradeability as a particular type of market illiquidity and investigate its impact on the price of…
The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes. The focus of our study is to give new characterizations of quasi self-duality for exponential L\'evy processes…
In this article we propose a study of market models starting from a set of axioms, as one does in the case of risk measures. We define a market model simply as a mapping from the set of adapted strategies to the set of random variables…
We suggest that Free Random Variables, represented here by large random matrices with spectral Levy disorder, may be relevant for several problems related to the modeling of financial systems. In particular, we consider a financial…
We study the Fundamental Theorem of Asset Pricing for a general financial market under Knightian Uncertainty. We adopt a functional analytic approach which require neither specific assumptions on the class of priors $\mathcal{P}$ nor on the…
We investigate the impossibility of universally winning trading strategies -- those generating strict profit across all market trajectories -- through three distinct mathematical paradigms. Fundamentally, under standard admissibility…