Learning the Efficient Frontier

The efficient frontier (EF) is a fundamental resource allocation problem where one has to find an optimal portfolio maximizing a reward at a given level of risk. This optimal solution is traditionally found by solving a convex optimization problem. In this paper, we introduce NeuralEF: a fast neural approximation framework that robustly forecasts the result of the EF convex optimization problem with respect to heterogeneous linear constraints and variable number of optimization inputs. By reformulating an optimization problem as a sequence to sequence problem, we show that NeuralEF is a viable solution to accelerate large-scale simulation while handling discontinuous behavior.

FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs

This paper introduces a new approach for generating sequences of implied volatility (IV) surfaces across multiple assets that is faithful to historical prices. We do so using a combination of functional data analysis and neural stochastic differential equations (SDEs) combined with a probability integral transform penalty to reduce model misspecification. We demonstrate that learning the joint dynamics of IV surfaces and prices produces market scenarios that are consistent with historical features and lie within the sub-manifold of surfaces that are free of static arbitrage.

Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders

We propose a hybrid method for generating arbitrage-free implied volatility (IV) surfaces consistent with historical data by combining model-free Variational Autoencoders (VAEs) with continuous time stochastic differential equation (SDE) driven models. We focus on two classes of SDE models: regime switching models and L\'evy additive processes. By projecting historical surfaces onto the space of SDE model parameters, we obtain a distribution on the parameter subspace faithful to the data on which we then train a VAE. Arbitrage-free IV surfaces are then generated by sampling from the posterior distribution on the latent space, decoding to obtain SDE model parameters, and finally mapping those parameters to IV surfaces.

Robust and Active Learning for Deep Neural Network Regression

We describe a gradient-based method to discover local error maximizers of a deep neural network (DNN) used for regression, assuming the availability of an "oracle" capable of providing real-valued supervision (a regression target) for samples. For example, the oracle could be a numerical solver which, operationally, is much slower than the DNN. Given a discovered set of local error maximizers, the DNN is either fine-tuned or retrained in the manner of active learning.