Related papers: Structure Preserving Equivalent Martingale Measure…
Motivated by applications for set containment problems, we consider the following fundamental problem: can we design set-to-vector functions so that the natural partial order on sets is preserved, namely $S\subseteq T \text{ if and only if…
In a Monte-Carlo test, the observed dataset is fixed, and several resampled or permuted versions of the dataset are generated in order to test a null hypothesis that the original dataset is exchangeable with the resampled/permuted ones.…
Consider additive functionals of a Markov chain $W_k$, with stationary (marginal) distribution and transition function denoted by $\pi$ and $Q$, say $S_n=g(W_1)+...+g(W_n)$, where $g$ is square integrable and has mean 0 with respect to…
Given a c\`adl\`ag process $X$ on a filtered measurable space, we construct a version of its semimartingale characteristics which is measurable with respect to the underlying probability law. More precisely, let $\mathfrak{P}_{sem}$ be the…
We derive a nonparametric higher-order asymptotic expansion for small-time changes of conditional characteristic functions of It\^o semimartingale increments. The asymptotics setup is of joint type: both the length of the time interval of…
We show that the left-monotone martingale coupling is optimal for any given performance function satisfying the martingale version of the Spence-Mirrlees condition, without assuming additional structural conditions on the marginals. We also…
In many practical applications, evaluating the joint impact of combinations of environmental variables is important for risk management and structural design analysis. When such variables are considered simultaneously, non-stationarity can…
Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on…
We study class of L\'{e}vy processes having distributions being indentifiable by moments. We define system of polynomial martingales \newline $\left\{ M_{n}(X_{t},t),\mathcal{F}_{\leq t}\right\} _{n\geq 1},$ where $% \mathcal{F}_{\leq t}$…
A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics at criticality. Requiring multiple SLEs to…
In this article, we show necessary and sufficient conditions for a function to transform a continuous Markov semimartingale to a semimartingale. As a result, the no-arbitrage principle guarantees the differentiability of asset prices with…
There are many environments in econometrics which require nonseparable modeling of a structural disturbance. In a nonseparable model with endogenous regressors, key conditions are validity of instrumental variables and monotonicity of the…
We extend a well-known theorem of Murski\v{\i} to the probability space of finite models of a system $\mathcal{M}$ of identities of a strong idempotent linear Maltsev condition. We characterize the models of $\mathcal{M}$ in a way that can…
We use the martingale method to discuss the relationship between mean-variance (MV) and monotone mean-variance (MMV) portfolio selections. We propose a unified framework to discuss the relationship in general financial markets without any…
Certain countably and finitely additive measures can be associated to a given nonnegative supermartingale. Under weak assumptions on the underlying probability space, existence and (non)uniqueness results for such measures are proven.
We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming…
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…
In this paper we present the asymptotic analysis of the realised quadratic variation for multivariate symmetric $\beta$-stable L\'evy processes, $\beta \in (0,2)$, and certain pure jump semimartingales. The main focus is on derivation of…
In a previous paper, we proved that for any submartingale $(X_t)_{t \geq 0}$ of class $(\Sigma)$, defined on a filtered probability space $(\Omega, \mathcal{F}, \mathbb{P}, (\mathcal{F}_t)_{t \geq 0})$, which satisfies some technical…
We propose a computationally straightforward test for the linearity of a spatial interaction function. Such functions arise commonly, either as practitioner imposed specifications or due to optimizing behaviour by agents. Our conditional…