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Asset liability management under sequential stochastic dominance constraints

Giorgio Consigli, Darinka Dentcheva, Francesca Maggioni, Giovanni Micheli

TL;DR

The paper addresses long-horizon ALM for a financial intermediary facing multiple risk sources. It develops a multistage stochastic programming framework that combines a time-consistent dynamic risk measure in the objective with a time-consistent sequential second-order stochastic dominance funding constraint, showing that enforcing SSD at the $T-1$ stage guarantees ordering at all stages. A novel time-consistent, SSD-aware decomposition method is proposed to solve the MSP efficiently, integrating risk measures and event cuts for SSD. Computational validation on a property-and-casualty ALM case demonstrates that SSD constraints materially affect initial capital needs and solvency trajectories, especially under stressed liability scenarios, while preserving funding resilience through stage-by-stage planning.

Abstract

We consider a financial intermediary managing assets and liabilities exposed to several risk sources and seeking an optimal portfolio strategy to minimise the initial capital invested and the total risk associated with investment losses and financial debt. We formulate the problem as a multistage stochastic programming model, with a time-consistent dynamic risk measure in the objective function to control the investment risk. To ensure that the intermediary's financial equilibrium is preserved, we introduce a funding constraint in the model by enforcing in a time-consistent manner a sequential second-order stochastic dominance (SSD) of the portfolio return distribution over the liability distribution. We demonstrate that imposing the SSD constraint at the last-but-one stage is sufficient to enforce the SSD ordering at each stage. To deal with the computational burden of associated MSP, we develop a novel decomposition scheme integrating, for the first time in the literature, time-consistent dynamic risk measures and sequential stochastic dominance constraints. The proposed methodology is computationally validated on a case study developed on a property and casualty ALM problem.

Asset liability management under sequential stochastic dominance constraints

TL;DR

The paper addresses long-horizon ALM for a financial intermediary facing multiple risk sources. It develops a multistage stochastic programming framework that combines a time-consistent dynamic risk measure in the objective with a time-consistent sequential second-order stochastic dominance funding constraint, showing that enforcing SSD at the stage guarantees ordering at all stages. A novel time-consistent, SSD-aware decomposition method is proposed to solve the MSP efficiently, integrating risk measures and event cuts for SSD. Computational validation on a property-and-casualty ALM case demonstrates that SSD constraints materially affect initial capital needs and solvency trajectories, especially under stressed liability scenarios, while preserving funding resilience through stage-by-stage planning.

Abstract

We consider a financial intermediary managing assets and liabilities exposed to several risk sources and seeking an optimal portfolio strategy to minimise the initial capital invested and the total risk associated with investment losses and financial debt. We formulate the problem as a multistage stochastic programming model, with a time-consistent dynamic risk measure in the objective function to control the investment risk. To ensure that the intermediary's financial equilibrium is preserved, we introduce a funding constraint in the model by enforcing in a time-consistent manner a sequential second-order stochastic dominance (SSD) of the portfolio return distribution over the liability distribution. We demonstrate that imposing the SSD constraint at the last-but-one stage is sufficient to enforce the SSD ordering at each stage. To deal with the computational burden of associated MSP, we develop a novel decomposition scheme integrating, for the first time in the literature, time-consistent dynamic risk measures and sequential stochastic dominance constraints. The proposed methodology is computationally validated on a case study developed on a property and casualty ALM problem.

Paper Structure

This paper contains 17 sections, 1 theorem, 41 equations, 9 figures, 15 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Sequential stochastic dominance
  3. Asset-liability management: problem description and formulation
  4. Uncertainty model
  5. Yield curve, inflation and credit spread models
  6. Liability model
  7. Asset and currency returns
  8. Solution method
  9. Computational evidence
  10. Data inputs and experimental design
  11. Problem decomposition: numerical results
  12. Risk preferences, optimal debt exposure and initial capital allocation
  13. Control of interest rate risk
  14. Multi-period stochastic dominance and funding conditions
  15. Conclusions
  16. ...and 2 more sections

Key Result

Theorem 1

The dynamic order long-ssd holds provided holds for almost all $\xi_{[T-1]}$.

Figures (9)

  • Figure 1: Liability estimates $\Lambda_n=\sum_{j \in {\cal J}} \lambda_{j,n}, n \in {\cal N}_t, t\in{\cal T}$ in the ongoing business scenario (left) and in the stressed liability scenario (right).
  • Figure 2: Ongoing Business
  • Figure 3: Stressed Liability
  • Figure 5: Percentage of nodes with specific assets-liabilities duration mismatches at different stages for the ongoing business case (left), the stressed liability case with 6-month maximum mismatch (center) and the stressed liability case with 3-month maximum mismatch (right).
  • Figure 6: First order and second order CDFs for liabilities (red solid lines) and asset portfolios with (solid blue line) and without (dotted black line) SD constraints in representative nodes at different stages in the ongoing business scenario.
  • ...and 4 more figures

Theorems & Definitions (4)

  • Definition 1
  • Definition 2
  • Theorem 1
  • proof