Paper: arXiv 2603.19414

Authors: Brandon Tam, Mario Ghossoub, Silvana M. Pesenti

Abstract

We study a problem of optimal allocation in a discrete-time multi-period pure-exchange economy, where agents have preferences over stochastic endowment processes that are represented by strongly time-consistent dynamic risk measures. We introduce the notion of dynamic Pareto-optimal allocation processes and show that such processes can be constructed recursively starting with the allocation at the terminal time. We further derive a comonotone improvement theorem for allocation processes, and we provide a recursive approach to constructing comonotone dynamic Pareto optima when the agents’ preferences are coherent and satisfy a property that we call equidistribution-preserving. In the special case where each agent’s dynamic risk measure is of the distortion type, we provide a closed-form characterization of comonotone dynamic Pareto optima. We illustrate our results in a two-period setting.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents rigorous mathematical foundations for multi-period risk allocation using strongly time-consistent dynamic risk measures and comonotone improvements. While highly novel and mathematically dense in theoretical general equilibrium theory, it lacks any empirical backtesting, empirical validation, or real-world data analysis.

Research Flowchart

  flowchart TD
    A[Research Goal: Construct Dynamic Pareto-Optimal Allocations in Multi-Period Pure-Exchange Economies] --> B[Data Inputs: Agents' Preferences via Time-Consistent Dynamic Risk Measures & Stochastic Endowments]
    B --> C[Recursive Backward Induction Strategy: Terminal Allocation to Initial Period]
    C --> D[Derive Comonotone Improvement Theorem for Allocation Processes]
    D --> E[Recursive Construction for Coherent & Equidistribution-Preserving Preferences]
    E --> F[Closed-Form Characterization for Distortion Risk Measures & 2-Period Example]
    F --> G[Outcome: Dynamic Pareto-Optimal & Comonotone Allocation Processes]

Cited References (61)

  1. E fficiency in P ure- E xchange E conomies With R isk- A verse M onetary U tilities (2026)
  2. O ptimal C apital and R isk A llocations for L aw-and C ash- I nvariant C onvex F unctions (2008)
  3. Q uantile- B ased R isk S haring (2018)
  4. P areto E fficiency for the C oncave O rder and M ultivariate C omonotonicity (2012)
  5. D ynamic M onetary R isk M easures for B ounded D iscrete- T ime P rocesses (2006)
  6. R isk- A verse D ynamic P rogramming for M arkov D ecision P rocesses (2010)
  7. U ncertainty P ropagation and D ynamic R obust R isk M easures (2024)
  8. C oherent M easures of R isk (1999)
and 53 more
  1. C onvex M easures of R isk and T rading C onstraints (2002)
  2. O n L aw I nvariant C oherent R isk M easures (2001)
  3. P areto E fficient I nsurance C ontracts when the I nsurer’s C ost F unction is D iscontinuous (2003)
  4. N on- A dditive M easure and I ntegral (1994)
  5. S tochastic O rders (2007)
  6. I ntroduction to the M athematics of A mbiguity (2004)
  7. E quilibrium in a R einsurance M arket (1962)
  8. T he S afety L oading of R einsurance P remiums (1960)
  9. T he T heory of S yndicates (1968)
  10. C o- M onotone A llocations, B ickel- L ehmann D ispersion and the A rrow- P ratt M easure of R isk A version (1994)
  11. A R eview of S ome R esults R elated to C omonotonicity (1997)
  12. C omonotonicity and P areto O ptimality, with A pplication to C ollaborative I nsurance (2025)
  13. S ubjective P robability and E xpected U tility W ithout A dditivity (1989)
  14. O ptimal R isk- S haring R ules and E quilibria with C hoquet- E xpected- U tility (2000)
  15. A mbiguity, U ncertainty A version and E quilibrium W elfare (2004)
  16. A mbiguity A version and T rade (2011)
  17. O ptimal A llocations with $\alpha$- M ax M in U tilities, C hoquet E xpected U tilities, and P rospect T heory (2023)
  18. O n E quilibria W hen A gents H ave M ultiple P riors (2002)
  19. M axmin E xpected U tility with N on- U nique P rior (1989)
  20. A mbiguity A version, R obustness, and the V ariational R epresentation of P references (2006)
  21. O verlapping R isk A djusted S ets of P riors and the E xistence of E fficient A llocations and E quilibria with S hort- S elling (2010)
  22. C omonotone P areto O ptimal A llocations for L aw I nvariant R obust U tilities on $L^1$ (2014)
  23. E fficient A llocations U nder A mbiguity (2011)
  24. W eighted C omonotonic R isk S haring U nder H eterogeneous B eliefs (2020)
  25. I nf- C onvolution, O ptimal A llocations, and M odel U ncertainty for T ail R isk M easures (2022)
  26. Q uantile- B ased R isk S haring with H eterogeneous B eliefs (2020)
  27. O ptimal R isk S haring for L aw I nvariant M onetary U tility F unctions (2008)
  28. S haring M odel U ncertainty (2026)
  29. A S mooth M odel of D ecision M aking U nder A mbiguity (2005)
  30. M odel and P redictive U ncertainty: A F oundation for S mooth A mbiguity P references (2022)
  31. T he D ynamics of E fficient I ntertemporal A llocations with M any A gents, R ecursive P references, and P roduction (1988)
  32. S tructure of P areto O ptima in an I nfinite- H orizon E conomy W here A gents H ave R ecursive P references (1990)
  33. S tructure of P areto O ptima when A gents H ave S tochastic R ecursive P references (1995)
  34. S ubstitution, R isk A version and the T emporal B ehaviour of C onsumption and A sset R eturns: A T heoretical F ramework (1989)
  35. I ntertemporal A sset P ricing U nder K nightian U ncertainty (2004)
  36. N onexpected U tility P references in a T emporal F ramework with an A pplication to C onsumption- S avings B ehaviour (1990)
  37. R ecursive U tility U nder U ncertainty (1991)
  38. T he D ynamics of R isk- S ensitive A llocations (2005)
  39. E xotic P references for M acroeconomists (2004)
  40. S tochastic D ifferential U tility (1992)
  41. A sset P ricing with S tochastic D ifferential U tility (1992)
  42. E fficient and E quilibrium A llocations with S tochastic D ifferential U tility (1994)
  43. E fficient I ntertemporal A llocations with R ecursive U tility (1998)
  44. D ynamic P ortfolio C hoice and R isk A version (2007)
  45. O ptimal C onsumption and P ortfolio S election with S tochastic D ifferential U tility (1999)
  46. O ptimal L ifetime C onsumption- P ortfolio S trategies U nder T rading C onstraints and G eneralized R ecursive P references (2003)
  47. L ifetime C onsumption- P ortfolio C hoice U nder T rading C onstraints, R ecursive P references, and N ontradeable I ncome (2005)
  48. O ptimality and S tate P ricing in C onstrained F inancial M arkets with R ecursive U tility U nder C ontinuous and D iscontinuous I nformation (2008)
  49. R isk B udgeting A llocation for D ynamic R isk M easures (2025)
  50. R einforcement L earning with D ynamic C onvex R isk M easures (2024)
  51. T ime C onsistency of D ynamic R isk M easures and D ynamic P erformance M easures G enerated by D istortion F unctions (2025)
  52. A U nified A pproach to T ime C onsistency of D ynamic R isk M easures and D ynamic P erformance M easures in D iscrete T ime (2018)
  53. R isk- A verse O ptimization and C ontrol (2024)

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