Benchmark-Neutral Risk-Minimization for Insurance Products and Nonreplicable Claims
The paper introduces benchmark-neutral pricing and hedging for nonreplicable insurance and pension liabilities using the Growth Optimal Portfolio as numeraire. Prices are lower than risk-neutral levels while avoiding first-kind arbitrage. Contributions include an equivalent BN measure, a martingale decomposition, and a risk-minimizing strategy with minimal value process. The setup adds working-capital metrics, a trigger refinancing rule, and diversification where quadratic variation scales like $1/m$. A Bessel-based GOP model shows risk-neutral measures can fail in practice.
What it examines
The paper proposes benchmark-neutral risk minimization for pricing and hedging nonreplicable claims, like long-term insurance. It uses the stock Growth Optimal Portfolio as numeraire and a benchmark-neutral measure, yielding minimal, practical prices. It derives hedges via martingale decompositions, manages working capital with a refinancing rule, and prevents first-kind insurance--finance arbitrage.
What it concludes
Findings show BN pricing equals minimal fair prices, gives implementable hedges, reduces capital needs via diversification, and avoids insurance--finance arbitrage. Applications: variable annuities, pensions, liability books, capital planning. Limits: assumes GOP existence and BN martingale property. Future work: regulatory integration, multiple numeraires, empirical calibration, operational backtesting.
Evidence objects
Researchers unveil benchmark-neutral pricing for long-term, nonreplicable insurance and pensions, using the Growth Optimal Portfolio as numeraire; BN prices undercut risk-neutral levels while averting insurance--finance arbitrage of the first kind.
key_findings bullet 1 · key_findings · validation V0
Framework includes equivalent BN measure from the GOP, martingale decomposition with orthogonality, and risk-minimizing strategy; toolkit adds working-capital metrics, critical-capital refinancing triggers, and diversification where quadratic variation shrinks like $1/m$.
key_findings bullet 2 · key_findings · validation V0
A tractable squared Bessel GOP model explains overpriced risk-neutral valuations; methods include change of numeraire, Girsanov, Kunita--Watanabe, stopping-time formulas; weaknesses include GOP existence and martingale reliance, frictions, limited calibration evidence.
key_findings bullet 3 · key_findings · validation V0
Extending benchmark-neutral pricing, the paper introduces BN risk-minimization for nonreplicable claims using the stock growth-optimal portfolio ($GOP$) as numeraire under the BN measure. It operationalizes BN ideas via practical hedging, working-capital monitoring, and refinancing algorithms, avoiding first-kind arbitrage. Impactful for long-term insurance liabilities, it broadens incomplete-market pricing/hedging beyond derivative-centric frameworks.
key_findings bullet 4 · key_findings · validation V0
Raw abstract and provenance
Mathematical and Physical Sciences; Financial Research Network (FIRN) -T Eisele , T Schmidt. Insurance-finance arbitrage. Mathematical Finance , volume 34 ,
Source row: 297 · abstract type: snippet