Decentralized Finance: A Market Mechanism for Cybersecurity Risk Insurance

Björn Hanneke · Goethe University Frankfurt

MARBLE 2026 · Limassol · Funded by the Gesellschaft für Risikomanagement und Regulierung e.V. (FIRM)

April 2026

$292M

Kelp DAO is exploited. The shortfall lands on Aave. Within days, a coalition of protocols and founders commits capital to restore it.

No contract obliged the coalition, and no premium had compensated its risk.

The pattern

Around $10B in exploit losses, and under 1% of TVL is insured

≈$10B

cumulative exploit losses; extraction is immediate and irreversible

<1%

of DeFi's TVL carries formal cover today

2.6% /yr

median realized premium on existing cover (Nexus Mutual)

Existing cover is bought by users; the protocol that controls security holds no stake in the policy
The Kelp DAO coalition shows a willingness to pay for systemic resilience; today it pays ex post and sets no price

This paper

The mechanism must solve three design problems

Problem 1 · Pricing

Hack risk has no actuarial table

Loss histories are sparse and heterogeneous; threats evolve faster than models recalibrate. Today, premiums come from assessors on thin data, at several percent per year.

Goal: prices that equal risk-neutral hack probabilities

Problem 2 · Capital

Risk capital leaves when risk rises

Fixed returns give capital no reason to stay in stress, so underwriting capacity is scarcest exactly when it is needed most.

Goal: LP returns that adjust dynamically to utilization and priced risk

Problem 3 · Incentives

Coverage creates moral hazard

An insured party invests less in its own security. Today's user-bought cover leaves the protocol, which controls security, without a stake in the policy.

Goal: coverage that preserves the incentive to invest in security

Problem 1 · Pricing

HACK token prices reveal market-implied hack probabilities

Goal

Prices equal risk-neutral hack probabilities

Enforced by

Competitive speculation; no-arbitrage in the binary set $\mathrm{HACK}+\mathrm{NOHACK}=\$1$

Dispersed security knowledge is revealed through trading, and traders are paid for it
The term structure yields $\hat\lambda$; aggregation gives the risk index $P_{\mathrm{risk}}$
Dedicated, operator-governed markets with permissioned access

Prices rise with maturity; fitting the term structure yields $\hat\lambda$ and, aggregated, $P_{\mathrm{risk}}$.

Problem 2 · Capital

The yield share adjusts LP returns to utilization and priced risk

Goal

LP capital earns more when it carries more

Enforced by

The yield-share function $\gamma$, a protocol rule measurable on-chain

$\gamma\,(U,\;P_{\mathrm{risk}})\in[0,1]$ — increasing in both arguments

$C_{\mathrm{LP}}$ — the risk capital liquidity providers supply to the insurance pool
$U = \mathrm{coverage} \,/\, C_{\mathrm{LP}}$ — utilization: aggregate outstanding coverage relative to that capital; high $U$ means capital is scarce
$P_{\mathrm{risk}}$ — the market-implied risk index aggregated from HACK prices
LP yield therefore rises through two channels: capital scarcity and market-priced risk

Problem 2 · Capital

The resulting capital adjustment is self-stabilizing

Self-stabilizing: returns above $r_{\mathrm{market}}+\rho_{\mathrm{LP}}$ attract capital, which lowers $U$ and compresses $\gamma$
Role separation: capital providers are barred from HACK positions and cannot hedge the insured exposure

Problem 3 · Incentives

The insured protocol posts the first-loss capital

Goal

Moral hazard prevention: covered protocols keep investing in security

Enforced by

Forfeitable first-loss collateral and security-scaled coverage

Coverage is concave in collateral: $\mathrm{coverage} = \mu\, C_{\mathrm{C}}^{\theta}(1+\xi)$, $\theta\in(0,1)$
Verifiable security investment raises $\xi$ and buys more coverage per dollar of collateral
In the no-hack state, protocols receive a share of pool yield, lowering their net cost of coverage

Losses hit the protocol's own collateral before any pool capital.

The mechanism

One capital pool connects protocols, LPs, and speculators

Solid arrows: unconditional flows. Dashed arrows: scenario-dependent — (1) no hack, (2) verified hack. Same composition as Fig. 1 in the paper.

Analytical results

Four results establish equilibrium, incentive compatibility, participation, and solvency

Theorem 1 · Existence

A Nash equilibrium exists for any continuous $\gamma(U,P_{\mathrm{risk}})\in[0,1]$ increasing in both arguments.

Prop. 1 · Incentive-compatible pricing

HACK prices equal risk-neutral exploit probabilities.

Prop. 2 · Participation & stability

A minimum yield share sustains LP participation; the feedback is self-stabilizing.

Prop. 3 · Solvency bound

Solvent with probability $\ge 1-\varepsilon$ whenever $U \le 1/(\psi_{1-\varepsilon}\, c_{\max})$.

All proofs in the online appendix (cited in the paper).

Analytical results · 1 of 4

Theorem 1 · A Nash equilibrium exists

Under quasi-concave payoffs, a Nash equilibrium $(C_{\mathrm{C}}^{*},\,C_{\mathrm{LP}}^{*},\,S^{*})$ exists for any continuous $\gamma(U,P_{\mathrm{risk}})\in[0,1]$ increasing in both arguments.

$\pi_{\mathrm{LP}} = \gamma\,(1-\varphi)\,Y_{\mathrm{total}} - p_{\mathrm{hack}}\,\mathbb{E}\bigl[(\min(\mathrm{coverage},\mathrm{Loss})-C_{\mathrm{C}})^{+}\bigr] - C_{\mathrm{LP}}\,\mathbb{E}[r_{\mathrm{market}}]$ (Eq. 11 — the protocol objective, Eq. 9, is analogous)

Prop. 1 pins HACK prices to risk-neutral probabilities; the pricing layer enters the game only through the continuous index $P_{\mathrm{risk}}$
Wealth constraints make strategy sets compact and convex; payoffs are continuous (coverage function, bounded $\gamma$)
Quasi-concavity in each player's own strategy: standard sufficient conditions for existence in continuous games apply

Analytical results · 2 of 4

Proposition 1 · Prices equal risk-neutral hack probabilities

Under competitive markets with risk-neutral speculators, equilibrium HACK prices reveal the risk-neutral probabilities of a material exploit.

$V_{\mathrm{HACK}}(T) = p_{\mathrm{hack}}(T)\cdot \mathrm{DF}(T), \qquad p_{\mathrm{hack}}(T) = 1 - e^{-\lambda T}$ (Eq. 12 — fair value of the binary claim)

Competitive trading among admitted speculators: beliefs and the implied probability converge
Complete binary set per expiry: $\mathrm{HACK}+\mathrm{NOHACK} = \$1$ enforces price conservation
Risk neutrality: the HACK price equals the risk-neutral exploit probability; misreporting beliefs is unprofitable

Analytical results · 3 of 4

Proposition 2 · A minimum yield share sustains stable participation

A minimum yield share $\gamma_{\min}$ sustains LP participation: $r_{\mathrm{LP}} \ge r_{\mathrm{market}} + \rho_{\mathrm{LP}}$. The capital–utilization–return feedback is self-stabilizing.

$\gamma_{\min} = \dfrac{C_{\mathrm{LP}}\,(r_{\mathrm{market}}+\rho_{\mathrm{LP}}) + p_{\mathrm{hack}}\,\mathbb{E}\bigl[(\min(\mathrm{coverage},\mathrm{Loss})-C_{\mathrm{C}})^{+}\bigr]}{(1-\varphi)\,r_{\mathrm{pool}}\,C_{\mathrm{total}}}$ (Eq. 14)

LP return: yield share net of expected covered losses beyond first-loss collateral, per unit of capital
Imposing the outside option $r_{\mathrm{market}}+\rho_{\mathrm{LP}}$ and solving for $\gamma$ yields the participation bound
Adjustment $\partial C_{\mathrm{LP}}/\partial t = \kappa_{\mathrm{LP}} C_{\mathrm{LP}}\,[\,r_{\mathrm{LP}}(U) - (r_{\mathrm{market}}+\rho_{\mathrm{LP}})\,]$ (Eq. 15): returns above the bound attract capital, utilization falls, the yield share compresses

Analytical results · 4 of 4

Proposition 3 · The dynamic cap enforces the solvency bound

The pool remains solvent with probability $\ge 1-\varepsilon$ whenever $U \le 1/(\psi_{1-\varepsilon}\, c_{\max})$; the dynamic cap $U_{\max}(t)$ can enforce this bound.

$\mathrm{payout}_{\max} \le \psi_{1-\varepsilon}\, c_{\max}\, U\, C_{\mathrm{LP}} \le C_{\mathrm{LP}} \;\Longleftrightarrow\; U \le \dfrac{1}{\psi_{1-\varepsilon}\, c_{\max}}$ (Eq. 17)

Single hack per epoch: the obligation is bounded by the largest coverage, at most $c_{\max}\cdot U\cdot C_{\mathrm{LP}}$
Bounding the payout by pool capital at the $(1-\varepsilon)$-quantile $\psi_{1-\varepsilon}$ of loss-to-coverage yields the utilization bound
With $k$ hacks per epoch, $c_{\max}$ becomes the sum of the $k$ largest coverage shares (online appendix)

Simulation

1,000 seeded runs over 500 heterogeneous protocols

1,000

seeded runs · 2 years · daily steps

500

heterogeneous protocols, Pareto TVL calibrated to DeFi

$250M

initial LP pool capital $C_{\mathrm{LP}}^{0}$

Hack arrivals: Gamma-driven Poisson, ≈5 system-wide hacks per run, median covered hack ≈ $7M
Replication package public: simulation code, SymPy verification of the analytical results, all outputs

Results · baseline

In the simulated baseline, the net cost of coverage turns negative

Run-level distributions across 1,000 runs: LP APY, protocol APY, empirical loss rate, net protocol cost, cumulative payouts.

68.45 bps/yr

loss rate on $5,815M covered-dollar-years

−60.46 bps/yr

net protocol cost of coverage: the yield share exceeds forfeitures plus opportunity cost

0 / 1,000

runs with insolvency

Median APY: LPs 10.55%, protocols 4.89% · $\bar U = 9.51$ vs. cap 21.2 · $\bar\gamma = 0.55$

Results · stress

Under 4× hack intensity, coverage is rationed and the pool stays solvent

256 bps/yr

claims under stress ($132M)

30% of days

dynamic cap binds (baseline: ≈7%)

0 / 1,000

runs with insolvency; every claim paid in full

Coverage issuance is increasingly rationed as utilization reaches the prudential cap
The cost of stress falls on returns: median LP APY −4.3%, so LPs genuinely bear the risk

Discussion

Open design questions and further research

Operator decentralization — verification runs off-chain via a trusted operator; licensing and multi-signature governance mitigate, DAO-based verification is a future iteration
Relaxing the idealizations — beyond the single-hack epoch ($k$-hack generalization in the appendix) and risk-neutral speculators; the stress test is a first probe
Collusion and manipulation control — arbitrage makes price manipulation costly, independent speculator pricing deters protocol–LP collusion; Sybil circumvention and insider access need operational enforcement
Operating the prediction markets — launch and rollover of quarterly expiries: batch auction or capped bonding curve at the bootstrap, seeded market-making, seed withdrawal at depth thresholds
Deployment — protocol-level speculator liquidity, a staged rollout from high-TVL protocols, regulatory clarity on event markets
Ongoing extensions — attacker cost economics with empirically retrieved loss severities, and an implementation of the mechanism as a dynamic attacker–mechanism game

Conclusion

The coalition that rescued Kelp DAO is this mechanism's natural LP base. The mechanism organizes the same capital ex ante and at market prices.

Equilibrium exists (Thm 1, Props 1–3) · in a stylized simulation the mechanism self-stabilizes and no insolvency occurs · runs on established prediction-market technology

Paper · code · online appendix: github.com/bhanneke/DeFi-Insurance-MARBLE2026
hanneke@wiwi.uni-frankfurt.de