Related papers: Deterministic criteria for the absence of arbitrag…
We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically, and options are available for static hedging. In a general measure-theoretic setting, we show that absence of arbitrage in a…
This paper concerns the sharp asymptotic profiles of the solution of a diffusive epidemic model with one free boundary and one fixed boundary which is subject to the homogeneous Dirichlet boundary condition and Neumann boundary condition,…
We prove a version of First Fundamental Theorem of Asset Pricing under transaction costs for discrete-time markets with dividend-paying securities. Specifically, we show that the no-arbitrage condition under the efficient friction…
We study the stability of several no-arbitrage conditions with respect to absolutely continuous, but not necessarily equivalent, changes of measure. We first consider models based on continuous semimartingales and show that no-arbitrage…
The basic question of delineating those statistical problems that are solvable without making any assumptions on the underlying data distribution has long animated statistics and learning theory. This paper characterizes when a convex…
No-Free-Lunch Theorems state, roughly speaking, that the performance of all search algorithms is the same when averaged over all possible objective functions. This fact was precisely formulated for the first time in a now famous paper by…
We study a class of free boundary problems of ecological models with nonlocal and local diffusions, which are natural extensions of free boundary problems of reaction diffusion systems in there local diffusions are used to describe the…
We establish the zero-diffusion limit for both continuous and discrete aggregation models over convex and bounded domains. Compared with a similar zero-diffusion limit derived in [44], our approach is different and relies on a coupling…
In this paper we study arbitrage theory of financial markets in the absence of a num\'eraire both in discrete and continuous time. In our main results, we provide a generalization of the classical equivalence between no unbounded profits…
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 introduce and study a class of free boundary models with "nonlocal diffusion", which are natural extensions of the free boundary models in Du and Lin [17] and elsewhere, where "local diffusion" is used to describe the population…
In this paper, a general framework is developed for continuous-time financial market models defined from simple strategies through conditional topologies that avoid stochastic calculus and do not necessitate semimartingale models. We then…
For a class of partially observed diffusions, conditions are given for the map from the initial condition of the signal to filtering distribution to be contractive with respect to Wasserstein distances, with rate which does not necessarily…
We study a class of free boundary systems with nonlocal diffusion, which are natural extensions of the corresponding free boundary problems of reaction diffusion systems. As before the free boundary represents the spreading front of the…
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…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
The choice of boundary condition makes an essential difference in the solution structure of diffusion equations. The Dirichlet and Neumann boundary conditions and their combination have been the most used, but their legitimacy has been…
We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviours, depending upon the limiting cases…
Noncolliding diffusion processes reported in the present paper are $N$-particle systems of diffusion processes in one-dimension, which are conditioned so that all particles start from the origin and never collide with each other in a finite…
This is part II of our study on the free boundary problems with nonlocal and local diffusions. In part I, we obtained the existence, uniqueness, regularity and estimates of global solution. In part II here, we show a spreading-vanishing…