Paper: arXiv 2601.02276

Authors: Wing Fung Chong, Roxana Dumitrescu, Gechun Liang, Kenneth Tsz Hin Ng

Abstract

This article constructs a forward exponential utility in a market with multiple defaultable risks. Using the Jacod-Pham decomposition for random fields, we first characterize forward performance processes in a defaultable market under the default-free filtration. We then construct a forward utility via a system of recursively defined, indexed infinite-horizon backward stochastic differential equations (BSDEs) with discounting, and establish the existence, uniqueness, and boundedness of their solutions. To verify the required (super)martingale property of the performance process, we develop a rigorous characterization of this property with respect to the general filtration in terms of a set of (in)equalities relative to the default-free filtration. We further extend the analysis to a stochastic factor model with ergodic dynamics. In this setting, we derive uniform bounds for the Markovian solutions of the infinite-horizon BSDEs, overcoming technical challenges arising from the special structure of the system of BSDEs in the defaultable setting. Passing to the ergodic limit, we identify the limiting BSDE and relate its constant to the risk-sensitive long-run growth rate of the optimal wealth process.

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a highly sophisticated theoretical framework using infinite-horizon and ergodic BSDEs alongside the Jacod-Pham decomposition to solve forward utility problems under multiple default risks. However, as a purely mathematical finance paper, it lacks empirical backtesting, market data validation, or algorithmic code implementations.

Research Flowchart

  flowchart TD
    A[Research Goal: Construct Forward Exponential Utility<br/>under Multiple Default Risks] --> B[Input: Defaultable Market Model &<br/>Jacod-Pham Random Field Decomposition]
    B --> C[Derive System of Recursively Defined,<br/>Indexed Infinite-Horizon BSDEs]
    C --> D[Prove Existence, Uniqueness & Boundedness<br/>of BSDE Solutions under Default-Free Filtration]
    D --> E[Establish Super-martingale Verification Property<br/>under General Defaultable Filtration]
    E --> F[Extend to Stochastic Factor Model &<br/>Analyze Ergodic Limits]
    F --> G[Outcome: Optimal Wealth Dynamics &<br/>Risk-Sensitive Long-Run Growth Rate]

Cited References (37)

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  4. Portfolio choice under dynamic investment performance criteria (2009)
  5. Portfolio Choice under Space-Time Monotone Performance Criteria (2010)
  6. INITIAL INVESTMENT CHOICE AND OPTIMAL FUTURE ALLOCATIONS UNDER TIME-MONOTONE PERFORMANCE CRITERIA (2011)
  7. Forward rank-dependent performance criteria: time-consistent investment under probability distortion (2021) — link
  8. Optimal investment in defined contribution pension schemes with forward utility preferences — → 2303.08462
and 29 more
  1. Forward indifference valuation of A merican options (2012)
  2. Forward exponential indifference valuation in an incomplete binomial model (2016) — link
  3. Dynamic preferences for popular investment strategies in pension funds (2016)
  4. Competition in fund management and forward relative performance criteria (2022) — link
  5. An ergodic BSDE approach to forward entropic risk measures: representation and large-maturity behavior (2019) — link
  6. Pricing and hedging equity-linked life insurance contracts beyond the classical paradigm: the principle of equivalent forward preferences (2019) — link
  7. Predictable forward performance processes: Infrequent evaluation and applications to human-machine interactions (2023) — link
  8. Personalized robo-advising: enhancing investment through client interaction (2022) — link
  9. Rank-dependent predictable forward performance processes — → 2403.16228
  10. An Exact Connection between Two Solvable SDE s and a Nonlinear Utility Stochastic PDE (2013)
  11. Asymptotic Analysis of Forward Performance Processes in Incomplete Markets and Their Ill-Posed HJB Equations (2016)
  12. Consistent utility of investment and consumption: a forward/backward SPDE viewpoint (2018)
  13. Representation of Homothetic Forward Performance Processes in Stochastic Factor Models via Ergodic and Infinite Horizon BSDE (2017)
  14. Predictable Forward Performance Processes: the Binomial Case (2020)
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  20. OPTIMAL INVESTMENT IN CREDIT DERIVATIVES PORTFOLIO UNDER CONTAGION RISK (2016) — link
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2 of 37 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.