  In corporate bond markets, which are mainly OTC markets, market makers play a
central role by providing bid and ask prices for a large number of bonds to
asset managers from all around the globe. Determining the optimal bid and ask
quotes that a market maker should set for a given universe of bonds is a
complex task. Useful models exist, most of them inspired by that of Avellaneda
and Stoikov. These models describe the complex optimization problem faced by
market makers: proposing bid and ask prices in an optimal way for making money
out of the difference between bid and ask prices while mitigating the market
risk associated with holding inventory. While most of the models only tackle
one-asset market making, they can often be generalized to a multi-asset
framework. However, the problem of solving numerically the equations
characterizing the optimal bid and ask quotes is seldom tackled in the
literature, especially in high dimension. In this paper, our goal is to propose
a numerical method for approximating the optimal bid and ask quotes over a
large universe of bonds in a model \`a la Avellaneda-Stoikov. Because we aim at
considering a large universe of bonds, classical finite difference methods as
those discussed in the literature cannot be used and we present therefore a
discrete-time method inspired by reinforcement learning techniques. More
precisely, the approach we propose is a model-based actor-critic-like algorithm
involving deep neural networks.
