Bank decisions without the optimizer: rules distilled from LLM agents hold annual ROE within 0.31 points across ten simulated bank-years
Synopsis
In a stylized euro-area bank model of deposit pricing and bond reinvestment, large language model agents play the bank and four customer types, and equation-based decision rules are estimated from their choices. On simulations not used for estimation, the final rule keeps annual ROE within 0.31 percentage points in ten Claude simulated bank-years, meeting every fit criterion in seven; the three failures all involve deposit runs. With GPT-5.5 the gap stays within 0.71 points, but only six of eighteen simulated bank-years meet all criteria.
Interpretation
Bank decisions can be approximated by a few conditional rules instead of re-solving the original optimization objective each period. The prior benchmark had the bank maximize a twelve-month earnings objective with penalties for departing from risk targets, searched over a pricing grid by coordinate search. Across ten held-out Claude simulated bank-years, the final rule EQ4 differs from the agent bank's annual ROE by at most 0.31 percentage points and meets all fit criteria in seven; the three failures are deposit-run years. On the same evaluations, a market-pricing heuristic passes four, while the original optimizer, direct regression and nearest-neighbour approximations pass zero, zero and one.
The rules switch by liquidity regime: near-market pricing in ordinary months, higher deposit rates and loan margins under stress, and reinvestment shifted toward short-duration assets. The regimes summarize choices that recur across eight development simulations of the agent bank rather than estimates of real bank behavior. In seven of those eight development simulations, fixed-rate loan margins average 22 to 43 basis points above market in normal months, and the stress premium on rate-sensitive deposits is about 50 basis points; applied to six simulated bank-years under reworded instructions, the rule keeps ROE within 0.30 points, passes all four years without a run and fails the two run years.
Customer responses elicited from the agents depend on instruction wording, and removing behavioral hints changes withdrawal magnitudes and fixed-rate borrower sensitivity. The original instructions stated deposit-flow caps and told fixed-rate borrowers that a margin above market reduces borrowing only mildly. Under neutral instructions in both model families, monthly withdrawals of rate-sensitive deposits under severe news fall from 27 to 28 percent to 12 to 14 percent, and the fixed-rate borrower coefficient rises from 0.14 to 1.11 for Claude and from 0.08 to 0.62 for GPT-5.5; with neutral-instruction customer equations, two months of severe news no longer push LCR below 100 percent.
Perspective
The conclusions are scoped to a stylized, predominantly deposit-funded euro-area bank: customer deposits are 88 percent of assets, against a comparison-sample median near 52 percent, so substantive interpretation is restricted to banks funded roughly two-thirds or more by customer deposits. The model is a twelve-month monthly leader-follower game with parallel rate shocks and an externally specified competitor-rate pass-through, excluding strategic competing banks, interbank contagion and crisis-resolution tools. Most evaluations fix equation-based customers and test only the bank decision rule, and most held-out years come from the Claude family.
No specification meets all fit criteria in deposit-run years, and the stress-time bond allocation shifts to floating-rate assets under reworded instructions and GPT-5.5, so that rule is not stable. Neutral instructions lower withdrawal magnitudes, meaning the persistence of withdrawals after an LCR breach depends on the levels supplied by the original instructions. Cross-family pass counts, seven for Claude and six for GPT-5.5, rest on small samples and are not read as precise between-family differences. The model does not directly validate the behavior of real bank managers, borrowers or depositors.