PNL-Haircut Domain in Perpetual Futures

• The PNL-haircut domain is defined as a feasible budget-allocation problem that reallocates positive unrealized PNL in ADL rounds to restore exchange solvency.
• The framework models the sequential online-learning problem by integrating severity selection and account-level capacity constraints with various allocation mechanisms such as queue-based and pro-rata methods.
• Empirical case studies, including the Hyperliquid stress episode, demonstrate that smoother allocation policies significantly reduce overshoot and concentration compared to fixed queue methods.

The PNL-haircut domain is the formal action space introduced for autodeleveraging (ADL) in perpetual futures markets, where an exchange restores solvency by haircutting positive unrealized profit-and-loss (PNL) of profitable accounts rather than posted collateral principal (Chitra et al., 16 Feb 2026). In this formulation, each ADL round selects a solvency budget and an allocation of account-level PNL seizures subject to per-account capacity constraints, so that ADL becomes a sequential control problem with explicit objectives for solvency recovery, overshoot control, and burden concentration. The domain is therefore not a generic “haircut” framework, but a specific online-learning abstraction for last-resort loss socialization on winner-side gains (Chitra et al., 16 Feb 2026).

1. Scope and terminological boundaries

Within the supplied literature, the phrase “PNL-haircut domain” is formalized in the ADL setting of perpetual futures exchanges. In that setting, “PNL” refers to positive unrealized gains, and the haircut is imposed on those gains as part of a solvency-restoration mechanism (Chitra et al., 16 Feb 2026). The paper is explicit that “ADL haircuts apply to positive PNL (unrealized gains), not to posted collateral principal,” and also that it uses “strict PNL-only haircuts: ADL reallocates positive PNL and does not haircut protected collateral” (Chitra et al., 16 Feb 2026).

This meaning should be distinguished from unrelated arXiv usages of the same acronym. In logic, PNL denotes Permissive-Nominal Logic, and the relevant papers explicitly state that they do not introduce a formally named “haircut domain”; the nearest constructions there concern permission sets, support restrictions, and restricted quantification domains rather than any exchange-loss-allocation mechanism (Dowek et al., 2011, Dowek et al., 2023). In another line of work, PNL denotes positive and negative relations logic, again unrelated to haircuting of unrealized gains (Freiman et al., 2024). Elsewhere, PNL denotes Point-Neighborhood Learning for image segmentation, which is also unrelated to ADL (Jie et al., 2024). The term “haircut” is likewise polysemous across repo, securities lending, and literal hair or hairstyle modeling, but those uses refer to collateral valuation, grooming, or reconstruction rather than winner-side PNL seizure (Lou, 2016, Lou, 2021, Sklyarova et al., 2023).

2. Formal definition of the domain

The domain is built on an account-level representation

$$\mathfrak{p}_{i,t}=\big(q_{i,t},\bar p_{i,t},c_{i,t},\mathrm{PNL}_{i,t},e_{i,t}\big),$$

with active positions

$$\mathcal{P}_t=\{\mathfrak{p}_{i,t}: i\in\mathcal{I}_t\},$$

and trader equity

$e_{i,t}=c_{i,t}+\mathrm{PNL}_{i,t}.$

Venue solvency is

$\mathsf{Solv}_t(\mathcal P_t)=A_t^x-L_t^x,$

equivalently

$$\mathsf{Solv}_t(\mathcal P_t)=\sum_{\mathfrak p\in \mathcal P_t} e_t(\mathfrak p) =\sum_{i\in\mathcal I_t} e_{i,t},$$

with residual shortfall

$S_t=\big(-\mathsf{Solv}_t(\mathcal P_t)\big)_+.$

For ADL, the operative loser-side deficit is

$$D_t=\sum_{j\in L_t}\big(-e_{j,t}(p^{\mathrm{liq,exec}}(\mathfrak{p}_{j,t}, q_{j,t}))\big)_+.$$

The profitable accounts are

$$W_t=\{i\in\mathcal{I}_t:\mathfrak{p}_{i,t}\in\mathcal{P}_t,\ \mathrm{PNL}_{i,t}>0\},$$

and each has PNL haircut capacity

$$u_{i,t}=(\mathrm{PNL}_{i,t})_+, \qquad U_t=\sum_{i\in W_t}u_{i,t}.$$

The defining feature of the domain is that the action can only reallocate these positive-PNL capacities. Let $x_{i,t}$ denote the amount haircut from winner $$\mathcal{P}_t=\{\mathfrak{p}_{i,t}: i\in\mathcal{I}_t\},$$0 in round $$\mathcal{P}_t=\{\mathfrak{p}_{i,t}: i\in\mathcal{I}_t\},$$1. Then

$$\mathcal{P}_t=\{\mathfrak{p}_{i,t}: i\in\mathcal{I}_t\},$$2

The exchange’s round action is a pair $$\mathcal{P}_t=\{\mathfrak{p}_{i,t}: i\in\mathcal{I}_t\},$$3, where $$\mathcal{P}_t=\{\mathfrak{p}_{i,t}: i\in\mathcal{I}_t\},$$4 is the aggregate solvency budget and $$\mathcal{P}_t=\{\mathfrak{p}_{i,t}: i\in\mathcal{I}_t\},$$5 is the account-level allocation. The feasible action set is

$$\mathcal{P}_t=\{\mathfrak{p}_{i,t}: i\in\mathcal{I}_t\},$$6

This is the formal PNL-haircut domain: a budgeted redistribution problem over winner-side unrealized gains (Chitra et al., 16 Feb 2026).

Symbol	Meaning
$$\mathcal{P}_t=\{\mathfrak{p}_{i,t}: i\in\mathcal{I}_t\},$$7	residual loser-side deficit
$$\mathcal{P}_t=\{\mathfrak{p}_{i,t}: i\in\mathcal{I}_t\},$$8	profitable accounts with $$\mathcal{P}_t=\{\mathfrak{p}_{i,t}: i\in\mathcal{I}_t\},$$9
$e_{i,t}=c_{i,t}+\mathrm{PNL}_{i,t}.$0	account $e_{i,t}=c_{i,t}+\mathrm{PNL}_{i,t}.$1’s positive-PNL haircut capacity
$e_{i,t}=c_{i,t}+\mathrm{PNL}_{i,t}.$2	aggregate solvency budget chosen for the round
$e_{i,t}=c_{i,t}+\mathrm{PNL}_{i,t}.$3	haircut allocated to winner $e_{i,t}=c_{i,t}+\mathrm{PNL}_{i,t}.$4
$e_{i,t}=c_{i,t}+\mathrm{PNL}_{i,t}.$5	feasible budget-allocation set

The paper also gives an equivalent severity parameterization: $e_{i,t}=c_{i,t}+\mathrm{PNL}_{i,t}.$6 and

$e_{i,t}=c_{i,t}+\mathrm{PNL}_{i,t}.$7

Operationally, the venue first chooses how much of the observed deficit to socialize this round, then chooses how that burden is distributed across winners.

3. Sequential online-learning formulation

The state observed at round $e_{i,t}=c_{i,t}+\mathrm{PNL}_{i,t}.$8 is

$e_{i,t}=c_{i,t}+\mathrm{PNL}_{i,t}.$9

where $\mathsf{Solv}_t(\mathcal P_t)=A_t^x-L_t^x,$0 collects auxiliary round-start observables such as “price and volatility snapshots, spread/depth summaries, and recent liquidation-flow aggregates” (Chitra et al., 16 Feb 2026). A policy is history-dependent: $\mathsf{Solv}_t(\mathcal P_t)=A_t^x-L_t^x,$1 State transitions follow

$\mathsf{Solv}_t(\mathcal P_t)=A_t^x-L_t^x,$2

with shock $\mathsf{Solv}_t(\mathcal P_t)=A_t^x-L_t^x,$3.

A central modeling distinction is between the ex ante estimate of required ADL and the ex post amount actually needed after liquidation execution prices are realized. The ex ante target is

$\mathsf{Solv}_t(\mathcal P_t)=A_t^x-L_t^x,$4

whereas the replay benchmark is

$\mathsf{Solv}_t(\mathcal P_t)=A_t^x-L_t^x,$5

This distinction is what makes the problem online rather than static: the venue chooses $\mathsf{Solv}_t(\mathcal P_t)=A_t^x-L_t^x,$6 and $\mathsf{Solv}_t(\mathcal P_t)=A_t^x-L_t^x,$7 using only round-start information, but performance is evaluated using ex post realized execution.

The paper first introduces an asymmetric loss

$\mathsf{Solv}_t(\mathcal P_t)=A_t^x-L_t^x,$8

with

$\mathsf{Solv}_t(\mathcal P_t)=A_t^x-L_t^x,$9

Its deployed convex surrogate is

$$\mathsf{Solv}_t(\mathcal P_t)=\sum_{\mathfrak p\in \mathcal P_t} e_t(\mathfrak p) =\sum_{i\in\mathcal I_t} e_{i,t},$$0

The first term penalizes tracking error in solvency restoration; the second penalizes concentration of burden on the most heavily hit winner. The paper notes that, under exact execution, $$\mathsf{Solv}_t(\mathcal P_t)=\sum_{\mathfrak p\in \mathcal P_t} e_t(\mathfrak p) =\sum_{i\in\mathcal I_t} e_{i,t},$$1, so tracking error is mostly a severity-selection problem, whereas queue-versus-pro-rata design primarily affects the fairness/concentration term (Chitra et al., 16 Feb 2026).

4. Mechanism classes on the domain

A single ADL round has a three-part execution lifecycle. First, the venue measures residual loser-side deficit $$\mathsf{Solv}_t(\mathcal P_t)=\sum_{\mathfrak p\in \mathcal P_t} e_t(\mathfrak p) =\sum_{i\in\mathcal I_t} e_{i,t},$$2 and chooses a budget $$\mathsf{Solv}_t(\mathcal P_t)=\sum_{\mathfrak p\in \mathcal P_t} e_t(\mathfrak p) =\sum_{i\in\mathcal I_t} e_{i,t},$$3, or equivalently a severity $$\mathsf{Solv}_t(\mathcal P_t)=\sum_{\mathfrak p\in \mathcal P_t} e_t(\mathfrak p) =\sum_{i\in\mathcal I_t} e_{i,t},$$4 with $$\mathsf{Solv}_t(\mathcal P_t)=\sum_{\mathfrak p\in \mathcal P_t} e_t(\mathfrak p) =\sum_{i\in\mathcal I_t} e_{i,t},$$5. Second, it chooses winner-side reductions $$\mathsf{Solv}_t(\mathcal P_t)=\sum_{\mathfrak p\in \mathcal P_t} e_t(\mathfrak p) =\sum_{i\in\mathcal I_t} e_{i,t},$$6. Third, it matches winners and losers at loser bankruptcy transfer prices $$\mathsf{Solv}_t(\mathcal P_t)=\sum_{\mathfrak p\in \mathcal P_t} e_t(\mathfrak p) =\sum_{i\in\mathcal I_t} e_{i,t},$$7 (Chitra et al., 16 Feb 2026). The PNL-haircut domain accommodates several mechanism families.

Queue-based mechanisms assign a score $$\mathsf{Solv}_t(\mathcal P_t)=\sum_{\mathfrak p\in \mathcal P_t} e_t(\mathfrak p) =\sum_{i\in\mathcal I_t} e_{i,t},$$8, sort winners, and exhaust the budget greedily from the front of the queue. If $$\mathsf{Solv}_t(\mathcal P_t)=\sum_{\mathfrak p\in \mathcal P_t} e_t(\mathfrak p) =\sum_{i\in\mathcal I_t} e_{i,t},$$9 sorts scores in decreasing order, then the top-ranked accounts are fully haircutted,

$S_t=\big(-\mathsf{Solv}_t(\mathcal P_t)\big)_+.$0

until the budget is nearly filled; the marginal account may be partially haircutted, and all later accounts remain untouched. The paper emphasizes that this geometry can produce effectively $S_t=\big(-\mathsf{Solv}_t(\mathcal P_t)\big)_+.$1 haircuts for early queue positions (Chitra et al., 16 Feb 2026).

Partial-haircut policies distribute budget across many winners without fully exhausting each touched account. Writing

$S_t=\big(-\mathsf{Solv}_t(\mathcal P_t)\big)_+.$2

such policies aim for $S_t=\big(-\mathsf{Solv}_t(\mathcal P_t)\big)_+.$3, or enforce a cap $S_t=\big(-\mathsf{Solv}_t(\mathcal P_t)\big)_+.$4. This formulation assumes divisibility of PNL; the paper notes that integer contract granularity can complicate exact implementation (Chitra et al., 16 Feb 2026).

Pro-rata allocation is the canonical continuous fairness benchmark: $S_t=\big(-\mathsf{Solv}_t(\mathcal P_t)\big)_+.$5 It equalizes normalized burdens $S_t=\big(-\mathsf{Solv}_t(\mathcal P_t)\big)_+.$6 across all winners. The discrete counterpart is the integer min-max ILP

$S_t=\big(-\mathsf{Solv}_t(\mathcal P_t)\big)_+.$7

which minimizes the worst normalized burden subject to budget exactness and lot-feasible execution (Chitra et al., 16 Feb 2026).

This mechanism taxonomy matters because the domain itself does not impose queueing, pro-rata, or any specific fairness criterion. It only imposes the PNL-capacity constraints. Mechanism design then specifies how a feasible haircut vector $S_t=\big(-\mathsf{Solv}_t(\mathcal P_t)\big)_+.$8 is selected inside that domain.

5. Theoretical properties

The paper’s main performance theorem concerns the one-dimensional severity controller

$S_t=\big(-\mathsf{Solv}_t(\mathcal P_t)\big)_+.$9

with loss

$$D_t=\sum_{j\in L_t}\big(-e_{j,t}(p^{\mathrm{liq,exec}}(\mathfrak{p}_{j,t}, q_{j,t}))\big)_+.$$0

If the comparator path variation is

$$D_t=\sum_{j\in L_t}\big(-e_{j,t}(p^{\mathrm{liq,exec}}(\mathfrak{p}_{j,t}, q_{j,t}))\big)_+.$$1

projected OGD on $$D_t=\sum_{j\in L_t}\big(-e_{j,t}(p^{\mathrm{liq,exec}}(\mathfrak{p}_{j,t}, q_{j,t}))\big)_+.$$2 yields

$$D_t=\sum_{j\in L_t}\big(-e_{j,t}(p^{\mathrm{liq,exec}}(\mathfrak{p}_{j,t}, q_{j,t}))\big)_+.$$3

and, with

$$D_t=\sum_{j\in L_t}\big(-e_{j,t}(p^{\mathrm{liq,exec}}(\mathfrak{p}_{j,t}, q_{j,t}))\big)_+.$$4

$$D_t=\sum_{j\in L_t}\big(-e_{j,t}(p^{\mathrm{liq,exec}}(\mathfrak{p}_{j,t}, q_{j,t}))\big)_+.$$5

The result identifies the two core hardness parameters of repeated ADL: the scale of deficits and the path variation of the latent optimal severity (Chitra et al., 16 Feb 2026).

A second major result shows that fixed queue policies can incur linear regret. In a two-winner construction with alternating capacities

$$D_t=\sum_{j\in L_t}\big(-e_{j,t}(p^{\mathrm{liq,exec}}(\mathfrak{p}_{j,t}, q_{j,t}))\big)_+.$$6

budget $$D_t=\sum_{j\in L_t}\big(-e_{j,t}(p^{\mathrm{liq,exec}}(\mathfrak{p}_{j,t}, q_{j,t}))\big)_+.$$7, and fairness-only loss

$$D_t=\sum_{j\in L_t}\big(-e_{j,t}(p^{\mathrm{liq,exec}}(\mathfrak{p}_{j,t}, q_{j,t}))\big)_+.$$8

a fixed queue always serving account 1 first suffers

$$D_t=\sum_{j\in L_t}\big(-e_{j,t}(p^{\mathrm{liq,exec}}(\mathfrak{p}_{j,t}, q_{j,t}))\big)_+.$$9

This establishes that queue mechanisms can be structurally poor on the PNL-haircut domain even when total budget is exact.

The paper also decomposes total realized loss into online-control error and execution-estimation error: $$W_t=\{i\in\mathcal{I}_t:\mathfrak{p}_{i,t}\in\mathcal{P}_t,\ \mathrm{PNL}_{i,t}>0\},$$0 This makes robustness depend not only on the online algorithm but also on the quality of liquidation-execution estimation. The associated ex post failure metric is

$$W_t=\{i\in\mathcal{I}_t:\mathfrak{p}_{i,t}\in\mathcal{P}_t,\ \mathrm{PNL}_{i,t}>0\},$$1

which can remain large even when regret is small.

At the allocation level, the appendix formalizes the feasible haircut set for a fixed budget $$W_t=\{i\in\mathcal{I}_t:\mathfrak{p}_{i,t}\in\mathcal{P}_t,\ \mathrm{PNL}_{i,t}>0\},$$2 and capacities $$W_t=\{i\in\mathcal{I}_t:\mathfrak{p}_{i,t}\in\mathcal{P}_t,\ \mathrm{PNL}_{i,t}>0\},$$3 as the polytope

$$W_t=\{i\in\mathcal{I}_t:\mathfrak{p}_{i,t}\in\mathcal{P}_t,\ \mathrm{PNL}_{i,t}>0\},$$4

Queue allocations are shown to be extreme points of this polytope and to coincide with linear optimization over it. The paper then proves a sharp instability result: for every $$W_t=\{i\in\mathcal{I}_t:\mathfrak{p}_{i,t}\in\mathcal{P}_t,\ \mathrm{PNL}_{i,t}>0\},$$5, there exist score vectors $$W_t=\{i\in\mathcal{I}_t:\mathfrak{p}_{i,t}\in\mathcal{P}_t,\ \mathrm{PNL}_{i,t}>0\},$$6 with $$W_t=\{i\in\mathcal{I}_t:\mathfrak{p}_{i,t}\in\mathcal{P}_t,\ \mathrm{PNL}_{i,t}>0\},$$7 but

$$W_t=\{i\in\mathcal{I}_t:\mathfrak{p}_{i,t}\in\mathcal{P}_t,\ \mathrm{PNL}_{i,t}>0\},$$8

By contrast, the min-max burden problem

$$W_t=\{i\in\mathcal{I}_t:\mathfrak{p}_{i,t}\in\mathcal{P}_t,\ \mathrm{PNL}_{i,t}>0\},$$9

has unique optimizer

$$u_{i,t}=(\mathrm{PNL}_{i,t})_+, \qquad U_t=\sum_{i\in W_t}u_{i,t}.$$0

the pro-rata allocation. Every queue has strictly worse worst-burden,

$$u_{i,t}=(\mathrm{PNL}_{i,t})_+, \qquad U_t=\sum_{i\in W_t}u_{i,t}.$$1

In the language of the paper, this makes pro-rata the unique continuous optimizer of max-normalized fairness on the PNL-haircut domain (Chitra et al., 16 Feb 2026).

6. Hyperliquid stress episode

The empirical case study reconstructs the October 10, 2025 Hyperliquid stress episode over the window 21:16–21:27 UTC. The replay uses

$$u_{i,t}=(\mathrm{PNL}_{i,t})_+, \qquad U_t=\sum_{i\in W_t}u_{i,t}.$$2

ADL rounds and a total liquidation volume of

$$u_{i,t}=(\mathrm{PNL}_{i,t})_+, \qquad U_t=\sum_{i\in W_t}u_{i,t}.$$3

(Chitra et al., 16 Feb 2026). The replay holds fixed the realized round boundaries, loser deficits $$u_{i,t}=(\mathrm{PNL}_{i,t})_+, \qquad U_t=\sum_{i\in W_t}u_{i,t}.$$4, winner sets $$u_{i,t}=(\mathrm{PNL}_{i,t})_+, \qquad U_t=\sum_{i\in W_t}u_{i,t}.$$5, capacities $$u_{i,t}=(\mathrm{PNL}_{i,t})_+, \qquad U_t=\sum_{i\in W_t}u_{i,t}.$$6, observable context $$u_{i,t}=(\mathrm{PNL}_{i,t})_+, \qquad U_t=\sum_{i\in W_t}u_{i,t}.$$7, bankruptcy transfer prices $$u_{i,t}=(\mathrm{PNL}_{i,t})_+, \qquad U_t=\sum_{i\in W_t}u_{i,t}.$$8, and the realized market path. Counterfactual mechanisms therefore vary only in severity and allocation.

The paper reports the following aggregate quantities for the episode: $$u_{i,t}=(\mathrm{PNL}_{i,t})_+, \qquad U_t=\sum_{i\in W_t}u_{i,t}.$$9 The production queue’s overshoot relative to needed budget is reported as

$x_{i,t}$0

with a short-horizon sensitivity band of

$x_{i,t}$1

The calibrated instance-level upper envelope from the severity-regret proposition is

$x_{i,t}$2

using

$x_{i,t}$3

Against that benchmark, the production ADL queue causes about

$x_{i,t}$4

of regret, which the paper reports as approximately

$x_{i,t}$5

of the calibrated upper envelope. The best start-of-round baseline achieves

$x_{i,t}$6

or approximately

$x_{i,t}$7

of the same bound (Chitra et al., 16 Feb 2026).

Policy	Total objective
Production queue	\$64,859,522.21
Integer pro-rata	\$3,404,185.00
Vector mirror descent	\$4,413,367.61
Min-max ILP	\$106,205.81
Continuous pro-rata	\$2,732,437.29

The paper’s abstract states that “the best algorithm reduces overshoot to \$x_{i,t}$83.40M total objective and vector mirror descent at \$4.41M. The supplied details note a mild discrepancy between the abstract/introduction and the body on this point, and the distinction is material because the best deployable start-of-round baseline in the table is integer pro-rata rather than vector mirror descent (Chitra et al., 16 Feb 2026).

Substantively, the case study is used to argue that the production queue both over-socialized winner PNL and concentrated burden more heavily than smoother alternatives. In the paper’s interpretation, the domain therefore exposes a concrete exchange-design gap: queue-style ADL is feasible in the PNL-haircut domain, but it is not close to the best available use of that domain.

7. Relation to adjacent haircut literatures

The PNL-haircut domain belongs to the ADL literature, but it sits near several older haircut literatures in market microstructure and secured finance. In repo pricing, haircut is the discount from collateral market value used to determine cash lent, with economic capital identified as the main driver of repo spread and a negative linear relation between spread and haircut (Lou, 2016). In securities lending, haircut is excess collateralization, with indemnification priced as the sum of a risk charge, a capital charge, and a funding charge when the transaction haircut falls short of a target credit standard (Lou, 2021). In repo fire-sale network models, haircut or collateral valuation is made endogenous to aggregate liquidation, so that more sales worsen collateral value and force additional liquidation (Bichuch et al., 2020).

These adjacent literatures clarify what is distinctive about the ADL usage. In repo and securities lending, the haircut is applied to collateral valuation or overcollateralization. In the ADL domain, by contrast, the haircut applies to positive unrealized PNL, not to posted collateral principal (Chitra et al., 16 Feb 2026). A plausible implication is that the ADL formulation transfers the economic idea of a haircut from collateral-side credit protection to winner-side liability reduction: it is still a bounded haircut problem with budget, capacity, and fairness constraints, but the underlying object being haircut is a venue liability to profitable traders rather than collateral posted by a borrower.

That distinction also explains why the ADL paper formulates the problem as online learning. Repo and securities-lending haircut models center on loss distributions, economic capital, and pricing spreads (Lou, 2016, Lou, 2021), whereas the PNL-haircut domain centers on repeated severity selection, allocation across profitable accounts, and regret relative to an ex post solvency benchmark (Chitra et al., 16 Feb 2026). The family resemblance is therefore economic rather than terminological: each literature studies how a haircut governs residual loss absorption, but the ADL domain is the one that formalizes this explicitly on winner-side unrealized gains.

In that sense, the PNL-haircut domain can be defined compactly as the feasible budget-allocation space for haircuting positive unrealized PNL in repeated ADL rounds, together with the online decision problem of choosing severity and burden-sharing so as to recover exchange solvency with minimal tracking error and concentration (Chitra et al., 16 Feb 2026).