A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper shows real market exists free lunches with vanishing risks.
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 buy and selling the next period, with no shorting, and furthermore for weak conv…
We obtain a deterministic characterisation of the \emph{no free lunch with vanishing risk}, the \emph{no generalised arbitrage} and the \emph{no relative arbitrage} conditions in the one-dimensional diffusion setting and examine how these notions of no-arbitrage relate to each other.
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 maturities. Our framework is well adapted to the study of no-arbitrage properties and…
We derive deterministic criteria for the existence and non-existence of equivalent (local) martingale measures for financial markets driven by multi-dimensional time-inhomogeneous diffusions. Our conditions can be used to construct financial markets in which the \emph{no unbounded profit with bounded risk} condition ho…
We apply Geometric Arbitrage Theory to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation. We obtain closed form equations involving default intensities and loss given defaults characterizing the no-free-lunch-with-vanishing-risk condition …
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 processes of all other portfolios are supermartingales. Necessary and sufficient c…
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 arguments implicitly rely on conditions stronger than the No Free Lunch With Vanishing …
No free lunch theorem formalized for tensor network models.
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 Arbitrage and No Free Lunch with Vanishing Risk. We provide a complete characterisation…
The paper sets criteria for no arbitrage in complex financial models.
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 nor on the structure of the state space. Several aspects of modeling under Knightian Uncer…
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 the theory of Orlicz spaces. Moreover, various notions of no asymptotic arbitrage …
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 translate the property (NFLVR-S) in terms of so called structure conditions and we intr…
We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to: --Write arbitrage as curvature of a principal fibre bundle. --Parameterize arbitrage strategies by its holonomy. --Give the Fundamental Theorem of Asset …
This paper addresses the log-optimal portfolio for a general semimartingale model. The most advanced literature on the topic elaborates existence and characterization of this portfolio under no-free-lunch-with-vanishing-risk assumption (NFLVR). There are many financial models violating NFLVR, while admitting the log-op…
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 intact to the latter, avoiding some of the pitfalls of infinite-dimensional stochast…
We provide equivalence of numerous no-free-lunch type conditions for financial markets where the asset prices are modeled as exponential Levy processes, under possible convex constraints in the use of investment strategies. The general message is the following: if any kind of free lunch exists in these models it has to…
The study examines a financial model with sticky prices and finds no arbitrage when interest rate is zero.
Extends credit risky bond market models to include jumps and general semimartingales.
Double no-touch options, contracts which pay out a fixed amount provided an underlying asset remains within a given interval, are commonly traded, particularly in FX markets. In this work, we establish model-free bounds on the price of these options based on the prices of more liquidly traded options (call and digital …
No universal trading strategy exists due to mathematical impossibilities.
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 in Quantitative Finance. Formulating rigorously the exact definition of absence…
No free lunch theorems suggest inductive biases are needed, but we show neural networks prefer low-complexity data.
Unified models for asset prices with transaction costs and infinite variation strategies.
This paper extends results of Mortimer and Williams (1991) about changes of probability measure up to a random time under the assumptions that all martingales are continuous and that the random time avoids stopping times. We consider locally absolutely continuous measure changes up to a random time, changes of probabil…
The paper explores the limits of tight PAC-Bayes bounds for cheap models in robust statistics.
Paper explores rough path theory for frictionless markets, linking NCFL to unbiased rough integrators.
No free lunch theorems show all algorithms perform equally under uniform distribution.
This paper considers general term structure models like the ones appearing in portfolio credit risk modelling or life insurance. We give a general model starting from families of forward rates driven by infinitely many Brownian motions and an integer-valued random measure, generalizing existing approaches in the litera…
We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no-arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent conditions for its existence in terms of market. A good deal valuation is characterized …
Paper explores learning patterns in binary sequences, finding no method consistently outperforms others.
This paper considers an initial market model, specified by its underlying assets and its flow of information , and an arbitrary random time which might not be an -stopping time. As the death time and the default time (that might represent) can be seen when they occur only, the progress…
New bound limits generalization gap for large models, independent of model complexity.
Study examines insider trading in short-selling restricted markets.
Study reveals a hidden cost in derivatives markets through option-implied discount factors.
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 (even uncountably) infinite number of assets, as it is for instance the case in bond…
PPI++ outperforms gold-standard labels only if pseudo-labels are highly correlated.
Free lunch from noise reveals linear spectral features for RL.
This manuscript presents some new impossibility results on adversarial robustness in machine learning, a very important yet largely open problem. We show that if conditioned on a class label the data distribution satisfies the Talagrand transportation-cost inequality (for example, this condition is satisfied if t…
New supervised and unsupervised NFLTs for elliptical distributions.
Develops a stochastic approach to financial market delays.
The study examines how permutation-based optimization performance varies across different function representations.
Extends utility maximization theory for infinite horizons without strong no-arbitrage assumptions.
The study defines backdoor detection in ML and proves its infeasibility.
Study on RL on volatility surfaces, proving no free lunch for law-seeking methods.
The study examines markets with multiple numéraires and finds equivalent martingale measures.
MC Dropout is re-evaluated as not Bayesian, affecting predictive posterior and multimodality.