相关论文: A change of measure formula for recursive conditio…

The paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be…

The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…

Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing…

Different approaches to defining dynamic market risk measures are available in the literature. Most are focused or derived from probability theory, economic behavior or dynamic programming. Here, we propose an approach to define and…

Fractional Brownian motion has become a standard tool to address long-range dependence in financial time series. However, a constant memory parameter is too restrictive to address different market conditions. Here we model the price…

Treatment effects can be estimated from observational data as the difference in potential outcomes. In this paper, we address the challenge of estimating the potential outcome when treatment-dose levels can vary continuously over time.…

We study the properties of nonlinear Backward Stochastic Differential Equations (BSDEs) driven by a Brownian motion and a martingale measure associated with a default jump with intensity process $(\lambda_t)$. We give a priori estimates for…

We introduce a new class of forward performance processes that are endogenous and predictable with regards to an underlying market information set and, furthermore, are updated at discrete times. We analyze in detail a binomial model whose…

Modelling partial differential equations (PDEs) is of crucial importance in science and engineering, and it includes tasks ranging from forecasting to inverse problems, such as data assimilation. However, most previous numerical and machine…

We propose a framework to perform Bayesian inference using conditional score-based diffusion models to solve a class of inverse problems in mechanics involving the inference of a specimen's spatially varying material properties from noisy…

This paper presents a wp-style calculus for obtaining expectations on the outcomes of (mutually) recursive probabilistic programs. We provide several proof rules to derive one-- and two--sided bounds for such expectations, and show the…

We extend the notion of forward performance criteria to settings with random endowment in incomplete markets. Building on these results, we introduce and develop the novel concept of \textit{forward optimized certainty equivalent (forward…

Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…

This work develops asymptotic properties of a class of switching jump diffusion processes. The processes under consideration may be viewed as a number of jump diffusion processes modulated by a random switching mechanism. The underlying…

Recently, there has been a growing interest in generative models based on diffusions driven by the empirical robustness of these methods in generating high-dimensional photorealistic images and the possibility of using the vast existing…

We suggest a simple reduction of pricing European options in affine jump-diffusion models to pricing options with modified payoffs in diffusion models. The procedure is based on the conjugation of the infinitesimal generator of the model…

We derived similar to Bo et al. (2010) results but in the case when the dynamics of the FX rate is driven by a general Merton jump-diffusion process. The main results of our paper are as follows: 1) formulas for the Esscher transform…

Most previous contributions to BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to…

We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…

In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or non-random…