Related papers: Deterministic criteria for the absence of arbitrag…
We revisit mean-risk portfolio selection in a one-period financial market where risk is quantified by a positively homogeneous risk measure $\rho$. We first show that under mild assumptions, the set of optimal portfolios for a fixed return…
In this paper, we investigate a multi-dimensional nonlocal degenerate diffusion-aggregation equation with a diffusion exponent $m$ in the intermediate range $\frac{2d}{2d-\gamma}<m<\frac{d+\gamma}{d}$, where the nonlocal aggregation term is…
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear…
We provide a general framework for no-arbitrage concepts in topological vector lattices, which covers many of the well-known no-arbitrage concepts as particular cases. The main structural condition we impose is that the outcomes of trading…
Popular guidance for denoising diffusion probabilistic model (DDPM) linearly combines distinct conditional models together to provide enhanced control over samples. However, this approach overlooks nonlinear effects that become significant…
A noncolliding diffusion process is a conditional process of $N$ independent one-dimensional diffusion processes such that the particles never collide with each other. This process realizes an interacting particle system with long-ranged…
In this paper a finite discrete time market with an arbitrary state space and bid-ask spreads is considered. The notion of an equivalent bid-ask martingale measure (EBAMM) is introduced and the fundamental theorem of asset pricing is proved…
By considering an explicit nonequilibrium model, we analyze the statistics of the irreversible work, $w_{\rm irr}$, and irreversible entropy production, $\Delta_i s$, within the stochastic energetics framework. Restating the second law of…
We consider a one-dimensional diffusion process $(X_t)$ which is observed at $n+1$ discrete times with regular sampling interval $\Delta$. Assuming that $(X_t)$ is strictly stationary, we propose nonparametric estimators of the drift and…
The conditions for a generalized Burgers equation which a priori involves nine arbitrary functions of one, or two variables to allow an infinite dimensional symmetry algebra are determined. Though this algebra can involve up to two…
The problem of a nonrelativistic particle with an internal color degree of freedom, with and without spin, moving in a free random gauge background is discussed. Freeness is a concept developed recently in the mathematical literature…
The conditioning of the linear finite volume element discretization for general diffusion equations is studied on arbitrary simplicial meshes. The condition number is defined as the ratio of the maximal singular value of the stiffness…
We propose a generalized diffusion equation for a flat Euclidean space subjected to a continuous infinitesimal scale transform. For the special cases of an algebraic or exponential expansion/contraction, governed by time-dependent scale…
We study derivative-free methods for policy optimization over the class of linear policies. We focus on characterizing the convergence rate of these methods when applied to linear-quadratic systems, and study various settings of driving…
This work contributes to an understanding of the domain size's effect on the existence and uniqueness of the linear convection--diffusion equation with integral-type boundary conditions, where boundary conditions depend non-locally on…
We consider the van der Waals free energy functional in a bounded interval with inhomogeneous Dirichlet boundary conditions imposing the two stable phases at the endpoints. We compute the asymptotic free energy cost, as the length of the…
We prove that, for locally bounded processes, absence of arbitrage opportunities of the first kind is equivalent to the existence of a dominating local martingale measure. This is related to and motivated by results from the theory of…
The classical discrete time model of proportional transaction costs relies on the assumption that a feasible portfolio process has solvent increments at each step. We extend this setting in two directions, allowing for convex transaction…
Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with non-constant diffusivities are studied. The work is a natural continuation of our paper (Cherniha and Davydovych, 2012)…
We introduce a financial market model featuring a risky asset whose price follows a sticky geometric Brownian motion and a riskless asset that grows with a constant interest rate $r\in \mathbb R $. We prove that this model satisfies No…