Guillaume Broux-Quemerais,Sarah Kaakai, Anis Matoussi,Wissal Sabbagh

In this paper,we present a probabilistic numerical method for a class of forward utilities in a stochastic factor model.For this purpose,we use the representation of forward utilities using the ergodic Backward Stochastic Differential Equations(eBSDEs)introduced by Liang and Zariphopoulou in[27].We establish a connection between the solution of the ergodic BSDE and the solution of an associated BSDE with random terminal time T,defined as the hitting time of the positive recurrent stochastic factor.The viewpoint based on BSDEs with random horizon yields a new characterization of the ergodic cost^which is a part of the solution of the eBSDEs.In particular,for a certain class of eBSDEs with quadratic generator,the Cole-Hopf transformation leads to a semi-explicit representation of the solution as well as a new expression of the ergodic cost>.The latter can be estimated with Monte Carlo methods.We also propose two new deep learning numerical schemes for eBSDEs.Finally,we present numerical results for different examples of eBSDEs and forward utilities together with the associated investment strategies.

DeepPredict:A Zone Preference Prediction System for Online Lodging Platforms

Online lodging platforms have become more and more popular around the world.To make a booking in these platforms,a user usually needs to select a city first,then browses among all the prospective options.To improve the user experience,understanding the zone preferences of a user's booking behavior will be helpful.In this work,we aim to predict the zone preferences of users when booking accommodations for the next travel.We have two main challenges:(1)The previous works about next information of Points Of Interest(Pals)recommendation are mainly focused on users'historical records in the same city,while in practice,the historical records of a user in the same city would be very sparse.(2)Since each city has its own specific geographical entities,it is hard to extract the structured geographical features of accommodation in different cities.Towards the difficulties,we propose DeepPredict,a zone preference prediction system.To tackle the first challenge,DeepPredict involves users'historical records in all the cities and uses a deep learning based method to process them.For the second challenge,DeepPredict uses HERE places API to get the information of pals nearby,and processes the information with a unified way to get it.Also,the description of each accommodation might include some useful information,thus we use Sent2Vec,a sentence embedding algorithm,to get the embedding of accommodation description.Using a real-world dataset collected from Airbnb,DeepPredict can predict the zone preferences of users'next bookings with a remarkable performance.DeepPredict outperforms the state-of-the-art algorithms by 60%in macro Fl-score.