Paper: arXiv 2503.02697

Abstract

This paper investigates an infinite horizon, discounted, consumption-portfolio problem in a market with one bond, one liquid risky asset, and one illiquid risky asset with proportional transaction costs. We consider an agent with liquidity preference, modeled by a Cobb-Douglas utility function that includes the liquid wealth. We analyze the properties of the value function and divide the solvency region into three regions: the buying region, the no-trading region, and the selling region, and prove that all three regions are non-empty. We mathematically characterize and numerically solve the optimal policy and prove its optimality. Our numerical analysis sheds light on the impact of various parameters on the optimal policy, and some intuition and economic insights behind it are also analyzed. We find that liquidity preference encourages agents to retain more liquid wealth and inhibits consumption, and may even result in a negative allocation to the illiquid asset. The liquid risky asset not only affects the location of the three regions but also has an impact on consumption. However, whether this impact on consumption is promoted or inhibited depends on the degree of risk aversion of agents.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents heavy mathematical derivations including Hamilton-Jacobi-Bellman equations, singular stochastic control, and viscosity solutions for a multi-asset transaction cost problem. While it includes numerical analysis, the methodology is primarily theoretical with proofs and characterizations rather than backtested trading strategies or real-world data implementation.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Liquid vs Illiquid Asset Choice<br>with Liquidity Preference"] --> B["Methodology: Inertial-Consumption-Portfolio Model"]
  B --> C{"Data/Inputs"}
  C --> D1["Market: Bond & Risky Assets"]
  C --> D2["Agent: Liquidity Pref.<br>Cobb-Douglas Utility"]
  C --> D3["Constraint: Proportional<br>Transaction Costs"]
  D1 & D2 & D3 --> E["Computational Process:<br>Numerical Solution of<br>Value Function & Policy Rules"]
  E --> F["Key Findings/Outcomes"]
  F --> G1["Three Non-empty Regions<br>(Buy, Sell, No-trade)"]
  F --> G2["Liquidity Pref. →<br>Higher Liquid Wealth<br>& Lower Consumption"]
  F --> G3["Risky Asset Affects<br>Region Boundaries &<br>Consumption (depends on Risk Aversion)"]

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and 20 more
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0 of 28 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.