相关论文: Error calculus and path sensitivity in financial m…

Many modern computational approaches to classical problems in quantitative finance are formulated as empirical loss minimization (ERM), allowing direct applications of classical results from statistical machine learning. These methods,…

This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational…

Recent years have seen an increased level of interest in pricing equity options under a stochastic volatility model such as the Heston model. Often, simulating a Heston model is difficult, as a standard finite difference scheme may lead to…

We present a probabilistic formulation of risk aware optimal control problems for stochastic differential equations. Risk awareness is in our framework captured by objective functions in which the risk neutral expectation is replaced by a…

When an expert operates a perilous dynamic system, ideal constraint information is tacitly contained in their demonstrated trajectories and controls. The likelihood of these demonstrations can be computed, given the system dynamics and task…

Within the framework of the previous paper [8]. we develop a generalized stochastic calculus for processes associated to higher order diffusion operators. Applications to the study of a Cauchy problem, a Feynman-Kac formula and a…

We consider a general path-dependent version of the hedging problem with price impact of Bouchard et al. (2019), in which a dual formulation for the super-hedging price is obtained by means of PDE arguments, in a Markovian setting and under…

Sensitivity analysis is an important tool used in many domains of computational science to either gain insight into the mathematical model and interaction of its parameters or study the uncertainty propagation through the input-output…

Performing sensitivity analysis for influence diagrams using the decision circuit framework is particularly convenient, since the partial derivatives with respect to every parameter are readily available [Bhattacharjya and Shachter, 2007;…

The mathematical model of a linear system with the short memory about own stochastic behavior is proposed. It is assumed that the system is under a continual influence of independent stochastic impulses. In a short memory approximation the…

We provide an efficient method to approximate the covariance between decision variables and uncertain parameters in solutions to a general class of stochastic nonlinear complementarity problems. We also develop a sensitivity metric to…

Recent developments in deep learning techniques have motivated intensive research in machine learning-aided stock trading strategies. However, since the financial market has a highly non-stationary nature hindering the application of…

Derivative hedging and pricing are important and continuously studied topics in financial markets. Recently, deep hedging has been proposed as a promising approach that uses deep learning to approximate the optimal hedging strategy and can…

In this work we propose deep learning-based algorithms for the computation of systemic shortfall risk measures defined via multivariate utility functions. We discuss the key related theoretical aspects, with a particular focus on the…

The Pareto model is very popular in risk management, since simple analytical formulas can be derived for financial downside risk measures (Value-at-Risk, Expected Shortfall) or reinsurance premiums and related quantities (Large Claim Index,…

Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…

Optimal control of heterogeneous mean-field stochastic differential equations with common noise has not been addressed in the literature. In this work, we initiate the study of such models. We formulate the problem within a linear-quadratic…

Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…

There are various metrics for financial risk, such as value at risk (VaR), expected shortfall, expected/unexpected loss, etc. When estimating these metrics, it was very common to assume Gaussian distribution for the asset returns, which may…

Given the importance of continuous-time stochastic volatility models to describe the dynamics of interest rates, we propose a goodness-of-fit test for the parametric form of the drift and diffusion functions, based on a marked empirical…