# Deep Reinforcement Learning for Equal Risk Pricing and Hedging under Dynamic Expectile Risk Measures

arXiv: https://arxiv.org/abs/2109.04001 · HTML: https://mlsanity.com/paper/2109.04001/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 9 Sep 2021.

## Builds on (most cited first, 9 of 9)

- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Risk-sensitive Reinforcement Learning](https://mlsanity.com/paper/1311.2097/) (2013)
- [Policy Gradient for Coherent Risk Measures](https://mlsanity.com/paper/1502.03919/) (2015)
- [Risk-Averse Offline Reinforcement Learning](https://mlsanity.com/paper/2102.05371/) (2021)
- [Improving Robustness via Risk Averse Distributional Reinforcement Learning](https://mlsanity.com/paper/2005.00585/) (2020)
- [On the Convergence and Optimality of Policy Gradient for Markov Coherent Risk](https://mlsanity.com/paper/2103.02827/) (2021)
- [Practical Risk Measures in Reinforcement Learning](https://mlsanity.com/paper/1908.08379/) (2019)
- [Equal Risk Pricing and Hedging of Financial Derivatives with Convex Risk Measures](https://mlsanity.com/paper/2002.02876/) (2020)
- [Deep Equal Risk Pricing of Financial Derivatives with Multiple Hedging Instruments](https://mlsanity.com/paper/2102.12694/) (2021)

## Built on by (most cited first, 3 of 3)

- [Conditionally Elicitable Dynamic Risk Measures for Deep Reinforcement Learning](https://mlsanity.com/paper/2206.14666/) (2022)
- [Extreme Risk Mitigation in Reinforcement Learning using Extreme Value Theory](https://mlsanity.com/paper/2308.13011/) (2023)
- [RLOP: RL Methods in Option Pricing from a Mathematical Perspective](https://mlsanity.com/paper/2205.05600/) (2022)

## Abstract (arXiv)

Recently equal risk pricing, a framework for fair derivative pricing, was extended to consider dynamic risk measures. However, all current implementations either employ a static risk measure that violates time consistency, or are based on traditional dynamic programming solution schemes that are impracticable in problems with a large number of underlying assets (due to the curse of dimensionality) or with incomplete asset dynamics information. In this paper, we extend for the first time a famous off-policy deterministic actor-critic deep reinforcement learning (ACRL) algorithm to the problem of solving a risk averse Markov decision process that models risk using a time consistent recursive expectile risk measure. This new ACRL algorithm allows us to identify high quality time consistent hedging policies (and equal risk prices) for options, such as basket options, that cannot be handled using traditional methods, or in context where only historical trajectories of the underlying assets are available. Our numerical experiments, which involve both a simple vanilla option and a more exotic basket option, confirm that the new ACRL algorithm can produce 1) in simple environments, nearly optimal hedging policies, and highly accurate prices, simultaneously for a range of maturities 2) in complex environments, good quality policies and prices using reasonable amount of computing resources; and 3) overall, hedging strategies that actually outperform the strategies produced using static risk measures when the risk is evaluated at later points of time.