Deep learning for discrete-time hedging in incomplete markets

Simon Fecamp, Joseph Mikael and Xavier Warin

Abstract

This paper presents several algorithms based on machine learning to solve hedging problems in incomplete markets. The sources of incompleteness considered here are illiquidity, nontradable risk factors, discrete hedging dates and proportional transaction costs. Hedging strategies suggested by the algorithms introduced in this paper are compared with classical stochastic-control techniques on several payoffs using a mean squared error (MSE) criterion. Some of the proposed algorithms are flexible enough to deal with innovative loss criteria, and the profit and loss (P&L) distributions of the hedging strategies obtained with these new criteria are compared to the P&L distributions obtained with the classical MSE criterion. The most efficient algorithm is tested on a case with nonzero transaction costs, and we show how to obtain a whole Pareto frontier in a single training phase by randomly combining the criteria of average cost and variance during the learning phase.