Paper: arXiv 2601.10375

Authors: Beatrice Acciaio, Brandon Garcia Flores, Antonio Marini, Gudmund Pammer

Abstract

We formulate a dynamic reinsurance problem in which the insurer seeks to control the terminal distribution of its surplus while minimizing the L2-norm of the ceded risk. Using techniques from martingale optimal transport, we show that, under suitable assumptions, the problem admits a tractable solution analogous to the Bass martingale. We first consider the case where the insurer wants to match a given terminal distribution of the surplus process, and then relax this condition by only requiring certain moment or risk-based constraints.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a highly novel mathematical framework applying Martingale Optimal Transport (specifically Bass martingales) to dynamic reinsurance problems. However, it is a purely theoretical paper with high mathematical density and virtually no empirical backtesting or real-world data application in the provided text.

Research Flowchart

  flowchart TD
    A[Research Goal: Minimize L2-norm of ceded risk in dynamic reinsurance] --> B[Inputs: Surplus process & Terminal distribution/risk constraints]
    B --> C[Methodology: Apply Martingale Optimal Transport theory]
    C --> D[Computational Optimization: Formulate duality & solve via Bass martingale transport]
    D --> E[Outcome 1: Tractable optimal policy for exact terminal distribution matching]
    D --> F[Outcome 2: Relaxed optimal reinsurance under moment/risk-based constraints]

Cited References (67)

  1. Optimal reinsurance from an optimal transport perspective (2025)
  2. Lipschitz continuity of the Wasserstein projections in the convex order on the line (2023)
  3. Representation of Martingales with Jumps and Applications to Mathematical Finance (2004)
  4. Financial modelling with jump processes (2003)
  5. Self-decomposability and option pricing (2007)
  6. Decomposition of Random Variables and Vectors (Razlo \v z enija Slu \v c ajnych Veli \v c im i Vektorov, Engl.) By Ju. V. Linnik and IV Ostrovskii (1977)
  7. Additive normal tempered stable processes for equity derivatives and power-law scaling (2022)
  8. $ q $-Bass martingales (2024) — link
and 59 more
  1. The variance gamma (VG) model for share market returns (1990)
  2. The variance gamma process and option pricing (1998)
  3. Pricing American options under variance gamma (2004)
  4. Option pricing under the variance gamma process (2004)
  5. Explaining the characteristics of the power (CRRA) utility family (2008)
  6. Local Times and Excursion Theory for Brownian Motion (2013)
  7. A model-free version of the fundamental theorem of asset pricing and the super-replication theorem (2016)
  8. An extension of martingale transport and stability in robust finance — → 2304.09551
  9. A modern approach to probability theory (2013)
  10. Penalization of Barycenters in the Wasserstein Space (2019) — link
  11. Denseness of biadapted M onge mappings (2022) — link
  12. A Strong Law of Large Numbers for Positive Random Variables (2021) — link
  13. Irreducible convex paving for decomposition of multi-dimensional martingale transport plans (2017)
  14. Optimal portfolio choice and the valuation of illiquid securities (2001)
  15. Perforate and imperforate currency bands: Exchange rate management and the term structure of interest rate differentials (1990)
  16. Reflected Brownian motion in the “bang-bang” control of Brownian drift (1981)
  17. From the S chr"odinger problem to the M onge- K antorovich problem (2012) — link
  18. Generalized Wasserstein barycenters between probability measures living on different subspaces (2021) — link
  19. Computational optimal transport. With applications to data sciences (2018) — link
  20. Clustering Market Regimes using the Wasserstein Distance (2021) — link
  21. We can’t disagree forever (1982)
  22. The complexity of agreement (2005)
  23. Approximating common knowledge with common beliefs (1989)
  24. Common knowledge, communication, and convergence of beliefs (1984)
  25. The Measure Preserving Martingale Sinkhorn Algorithm (2023) — link
  26. Martingale S chr "o dinger bridges and optimal semistatic portfolios (2023) — link
  27. Model-free Hedging: A Martingale Optimal Transport Viewpoint (2017) — link
  28. OPTION PRICING WITH LINEAR MARKET IMPACT AND NONLINEAR B LACK- S CHOLES EQUATIONS (2018) — link
  29. Calibration of the Bass Local Volatility model (2023) — link
  30. The Martingale Sinkhorn Algorithm (2025) — link
  31. Measuring skewness and kurtosis (1984)
  32. What is kurtosis? An influence function approach (1987)
  33. Il problema dei pieni (1940)
  34. The safety loading of reinsurance premiums (1960)
  35. An attempt to determine the optimum amount of stop loss reinsurance (1960)
  36. Uncertainty and the welfare economics of medical care (1963)
  37. Optimal reinsurance (2009)
  38. Reinsurance: actuarial and statistical aspects (2017)
  39. On discrete-time dynamic programming in insurance: exponential utility and minimizing the ruin probability (2004)
  40. Optimal dynamic reinsurance (2006)
  41. Optimal dynamic risk control for insurers with state-dependent income (2014)
  42. Optimal proportional reinsurance policies in a dynamic setting (2001)
  43. Optimal dynamic XL reinsurance (2001)
  44. Optimal reinsurance and dividend distribution policies in the Cram 'e r-Lundberg model (2005)
  45. Optimal control of capital injections by reinsurance in a diffusion approximation (2009)
  46. Minimising expected discounted capital injections by reinsurance in a classical risk model (2011)
  47. Stochastic Control in Insurance (2007)
  48. Worst-case-optimal dynamic reinsurance for large claims (2012)
  49. Optimal investment for insurers (2000)
  50. Optimal dynamic reinsurance policies for large insurance portfolios (2003)
  51. Optimal investment for insurer with jump-diffusion risk process (2005)
  52. Optimal investment for an insurer to minimize its probability of ruin (2004)
  53. Optimal reinsurance under mean-variance premium principles (2001) — link
  54. Mean-variance optimal reinsurance arrangements (2004) — link
  55. Optimal reinsurance under variance related premium principles (2012) — link
  56. Optimal non-life reinsurance under Solvency II regime (2015) — link
  57. Pareto-optimal reinsurance under individual risk constraints (2022) — link
  58. Combining quota-share and excess of loss treaties on the reinsurance of $n$ independent risks (1991) — link
  59. Behavioral portfolio selection in continuous time (2008) — link

1 of 67 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.