Retail banks use Asset Liability Management (ALM) to hedge interest rate risk associated with differences in maturity and predictability of their loan and deposit portfolios. The opposing goals of profiting from maturity transformation and hedging interest rate risk while adhering to numerous regulatory constraints make ALM a challenging problem. We formulate ALM as a high-dimensional stochastic control problem in which monthly investment and financing decisions drive the evolution of the bank’s balance sheet. To find strategies that maximize long-term utility in the presence of constraints and stochastic interest rates, we train neural networks that parametrize the decision process. Our experiments provide practical insights and demonstrate that the approach of Deep ALM deduces dynamic strategies that outperform static benchmarks.