In this talk, we consider the problem of pricing and hedging an option in a data-driven incomplete market environment. We start by presenting the concept of equal risk pricing, which considers the fair price of an option to be the price that exposes both sides of the contract to the same level of risk. With a convex risk measure, this problem reduces to solving independently the writer and the buyer's hedging problem. The latter can be formulated using dynamic programming equations when the risk measure satisfies a Markovian property. Employing a worst-case risk measure, our first numerical study illustrates the advantages of equal risk pricing over schemes that only account for a pricing based on quadratic hedging (i.e., ϵ-arbitrage pricing), or pricing based on a fixed equivalent martingale measure (i.e., Black-Scholes pricing). Employing a dynamic expectile risk measure, we then extend for the first time the deep deterministic policy gradient algorithm, an off-policy actor-critic reinforcement learning (ACRL) algorithm, in order to train the risk averse dynamic hedging policies directly on trajectories of the asset. Our numerical experiments confirm that the new ACRL algorithm produces high quality solutions.

Bio: Erick Delage is a professor in the Department of Decision Sciences at HEC Montréal, a chairholder of the Canada Research Chair in decision making under uncertainty, and a member of the College of New Scholars, Artists and Scientists of the Royal Society of Canada. His research interests span the areas of robust and stochastic optimization, decision analysis, reinforcement learning, and risk management with applications to portfolio optimization, option pricing, inventory management, energy and transportation problems.