Related papers: Certifiably Pseudorandom Financial Derivatives
We propose a probabilistic framework for pricing derivatives, which acknowledges that information and beliefs are subjective. Market prices can be translated into implied probabilities. In particular, futures imply returns for these implied…
We investigate the probability of shadowing of a random finite pseudotrajectory by an exact trajectory for linear skew products. We describe general conditions under which a random pseudotrajectory can be shadowed with polynomial (with…
The importance of adequately modeling credit risk has once again been highlighted in the recent financial crisis. Defaults tend to cluster around times of economic stress due to poor macro-economic conditions, {\em but also} by directly…
For one-dimensional Schroedinger operators with complex-valued potentials, we construct pseudomodes corresponding to large pseudoeigenvalues. Our (non-semi-classical) approach results in substantial progress in achieving optimal conditions…
Proper econometric analysis should be informed by data structure. Many forms of financial data are recorded in discrete-time and relate to products of a finite term. If the data comes from a financial trust, it will often be further subject…
Pseudorandmness plays an important role in number theory, complexity theory and cryptography. Our aim is to use models of arithmetic to explain pseudorandomness by randomness. To this end we construct a set of models $\cal M$, a common…
Free differential algebras (FDA's) provide an algebraic setting for field theories with antisymmetric tensors. The "presentation" of FDA's generalizes the Cartan-Maurer equations of ordinary Lie algebras, by incorporating p-form potentials.…
The crux of semi-supervised semantic segmentation is to assign adequate pseudo-labels to the pixels of unlabeled images. A common practice is to select the highly confident predictions as the pseudo ground-truth, but it leads to a problem…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…
One of the most fundamental questions in quantitative finance is the existence of continuous-time diffusion models that fit market prices of a given set of options. Traditionally, one employs a mix of intuition, theoretical and empirical…
The 2008 financial crisis has been attributed to "excessive complexity" of the financial system due to financial innovation. We employ computational complexity theory to make this notion precise. Specifically, we consider the problem of…
In this article, we combine replication pricing with expectation pricing for derivative trades that are partially collateralized by cash. The derivatives are replicated by underlying assets and cash, using repurchasing agreement (repo) and…
Depending on the behaviour of the complex-valued electromagnetic potential in the neighbourhood of infinity, pseudomodes of one-dimensional Dirac operators corresponding to large pseudoeigenvalues are constructed. This is a first systematic…
We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and {\it vanishes} around the current price. This result is generic, and only relies on mild assumptions about the order flow…
We introduce a new stochastic duration model for transaction times in asset markets. We argue that widely accepted rules for aggregating seemingly related trades mislead inference pertaining to durations between unrelated trades: while any…
Given a pseudoword over suitable pseudovarieties, we associate to it a labeled linear order determined by the factorizations of the pseudoword. We show that, in the case of the pseudovariety of aperiodic finite semigroups, the pseudoword…
This paper presents a discrete--time equity derivatives pricing model with default risk in a no--arbitrage framework. Using the equity--credit reduced form approach where default intensity mainly depends on the firm's equity value, we…
Pseudo-labelling is a popular technique in unsuper-vised domain adaptation for semantic segmentation. However, pseudo labels are noisy and inevitably have confirmation bias due to the discrepancy between source and target domains and…
A negative basis trade enters a long bond position and buys protection on the issuer of the bond through credit default swap (CDS), aiming at arbitrage profit due to the bond-CDS basis. To classic reduced form model theorists, the existence…
The non-linear sewing lemma constructs flows of rough differential equations from a braod class of approximations called almost flows. We consider a class of almost flows that could be approximated by solutions of ordinary differential…