Related papers: Solving high-dimensional optimal stopping problems…
Consider the optimal stopping problem of a one-dimensional diffusion with positive discount. Based on Dynkin's characterization of the value as the minimal excessive majorant of the reward and considering its Riesz representation, we give…
Hedging exotic options in presence of market frictions is an important risk management task. Deep hedging can solve such hedging problems by training neural network policies in realistic simulated markets. Training these neural networks may…
The endeavor of artificial intelligence (AI) is to design autonomous agents capable of achieving complex tasks. Namely, reinforcement learning (RL) proposes a theoretical background to learn optimal behaviors. In practice, RL algorithms…
Auctions are widely used in exchanges to match buy and sell requests. Once the buyers and sellers place their requests, the exchange determines how these requests are to be matched. The two most popular objectives used while determining the…
In this work, we propose a new deep learning-based scheme for solving high dimensional nonlinear backward stochastic differential equations (BSDEs). The idea is to reformulate the problem as a global optimization, where the local loss…
Many decision problems in economics, information technology, and industry can be transformed to an optimal stopping of adapted random vectors with some utility function over the set of Markov times with respect to filtration build by the…
The great amount of datasets generated by various data sources have posed the challenge to machine learning algorithm selection and hyperparameter configuration. For a specific machine learning task, it usually takes domain experts plenty…
We introduce a machine-learning framework to learn the hyperparameter sequence of first-order methods (e.g., the step sizes in gradient descent) to quickly solve parametric convex optimization problems. Our computational architecture…
We present a parallel algorithm for solving backward stochastic differential equations (BSDEs in short) which are very useful theoretic tools to deal with many financial problems ranging from option pricing option to risk management. Our…
Although many well-known algorithms can solve each bipartite matching problem instance efficiently, it remains an open question how one could estimate the expected optimal matching distance for arbitrary numbers of randomly distributed…
Deep learning's success has been attributed to the training of large, overparameterized models on massive amounts of data. As this trend continues, model training has become prohibitively costly, requiring access to powerful computing…
The framework of deep operator network (DeepONet) has been widely exploited thanks to its capability of solving high dimensional partial differential equations. In this paper, we incorporate DeepONet with a recently developed policy…
We develop a novel deep learning approach for pricing European basket options written on assets that follow jump-diffusion dynamics. The option pricing problem is formulated as a partial integro-differential equation, which is approximated…
In this paper, it is shown that Bermudan option pricing based on either the r\'eduite (in a one-dimensional setting: piecewise harmonic interpolation) or cubature -- is sensible from an economic vantage point: Any sequence of thus-computed…
We present a new approximation scheme for the price and exercise policy of American options. The scheme is based on Hermite polynomial expansions of the transition density of the underlying asset dynamics and the early exercise premium…
We study optimal stopping for diffusion processes with unknown model primitives within the continuous-time reinforcement learning (RL) framework developed by Wang et al. (2020), and present applications to option pricing and portfolio…
Trajectory following is one of the complicated control problems when its dynamics are nonlinear, stochastic and include a large number of parameters. The problem has significant difficulties including a large number of trials required for…
Differential Dynamic Programming (DDP) has become a well established method for unconstrained trajectory optimization. Despite its several applications in robotics and controls however, a widely successful constrained version of the…
High-frequency trading is prevalent, where automated decisions must be made quickly to take advantage of price imbalances and patterns in price action that forecast near-future movements. While many algorithms have been explored and tested,…
In this paper, we investigate an interesting and important stopping problem mixed with stochastic controls and a \textit{nonsmooth} utility over a finite time horizon. The paper aims to develop new methodologies, which are significantly…