Related papers: A Heat Kernel Approach to Interest Rate Models
We establish a new formula for the heat kernel on regular trees in terms of classical I-Bessel functions. Although the formula is explicit, and a proof is given through direct computation, we also provide a conceptual viewpoint using the…
Earlier in the study of the combinatorial properties of the heat kernel of Laplace operator with covariant derivative diagram technique and matrix formalism were constructed. In particular, this formalism allows you to control the…
In this paper, we study two types of purely discontinuous symmetric Markov processes $X$ in bounded smooth subsets of $\mathbb R^d$: conservative processes and processes killed either upon approaching the boundary of the set or by a killing…
A susceptibility propagation that is constructed by combining a belief propagation and a linear response method is used for approximate computation for Markov random fields. Herein, we formulate a new, improved susceptibility propagation by…
We develop a general framework for incorporating distributional preferences in market design. We identify the structural properties of these preferences that guarantee the path independence of choice rules. In decentralized settings, a…
Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…
We develop a kernel method for generative modeling within the stochastic interpolant framework, replacing neural network training with linear systems. The drift of the generative SDE is $\hat b_t(x) = \nabla\phi(x)^\top\eta_t$, where…
We propose a framework for transfer learning of discount curves across different fixed-income product classes. Motivated by challenges in estimating discount curves from sparse or noisy data, we extend kernel ridge regression (KR) to a…
We use a powerful extension of the classical method of heat potentials, recently developed by the present author and his collaborators, to solve several significant problems of financial mathematics. We consider the following problems in…
Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…
Accurate approximations to density functionals have recently been obtained via machine learning (ML). By applying ML to a simple function of one variable without any random sampling, we extract the qualitative dependence of errors on…
In this paper, we consider a symmetric pure jump Markov process $X$ on a metric measure space with volume doubling conditions. Our focus is on estimating the transition density $p(t,x,y)$ of $X$ and studying its stability when the jumping…
We introduce a new strategy for compositional neural surrogates for radiation-matter interactions, a key task spanning domains from particle physics through nuclear and space engineering to medical physics. Exploiting the locality and the…
We propose a general framework for the simultaneous modeling of equity, government bonds, corporate bonds and derivatives. Uncertainty is generated by a general affine Markov process. The setting allows for stochastic volatility, jumps, the…
We propose a Markov jump process with the three-state herding interaction. We see our approach as an agent-based model for the financial markets. Under certain assumptions this agent-based model can be related to the stochastic description…
Kernels are powerful and versatile tools in machine learning and statistics. Although the notion of universal kernels and characteristic kernels has been studied, kernel selection still greatly influences the empirical performance. While…
This review summarizes the historical development of probability measures in asset pricing, from early mathematical finance and state price theory to risk-neutral valuation, martingale measures, forward measures, stochastic discount…
We show that not feeling the boundary estimates for heat kernels hold for any non-negative self-adjoint extension of the Laplace operator acting on vector-valued compactly supported functions on a domain in $\mathbb{R}^d$. They are…
Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…
Diffusion generative models have recently been applied to domains where the available data can be seen as a discretization of an underlying function, such as audio signals or time series. However, these models operate directly on the…