Paper: arXiv 2603.02820

Authors: Giorgio Ferrari, Tim Niclas Schütz

Abstract

In this paper, we study an intertemporal utility maximization problem in which an investor chooses consumption and portfolio strategies in the presence of a stochastic factor and a no-borrowing constraint. In the spirit of the Kim-Omberg model, the stochastic factor represents the expected excess return of the risky asset. It is perfectly negatively correlated with shocks to the risky asset, and follows an Ornstein-Uhlenbeck process, thereby capturing the mean reversion of expected excess returns-a feature well supported by empirical evidence in financial markets. The investor seeks to maximize expected utility from consumption, subject to the constraint that wealth remains nonnegative at all times. To address the dynamic no-borrowing constraint, we use Lagrange duality to transform the primal problem into a singular control problem in the dual space. We then characterize the solution to the dual singular control problem via an auxiliary two-dimensional optimal stopping problem featuring stochastic volatility, and subsequently retrieve the primal value function as well as the optimal portfolio and consumption plans. Finally, a numerical study is conducted to derive economic and financial implications.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework combining Lagrange duality, singular stochastic control, and two-dimensional optimal stopping with stochastic volatility to solve a dynamic consumption-portfolio problem under borrowing constraints. However, it is purely mathematical/theoretical with no empirical validation or backtesting, relying only on qualitative numerical illustrations.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve Kim-Omberg optimal consumption & portfolio problem with no-borrowing constraint] --> B[Inputs: OU Process for expected excess returns & CRRA Utility]
    B --> C[Step 1: Apply Lagrange Duality to transform primal problem into dual singular control]
    C --> D[Step 2: Characterize dual problem via auxiliary 2D optimal stopping problem]
    D --> E[Step 3: Solve optimal stopping problem & retrieve primal value function, portfolio, and consumption]
    E --> F[Outcomes & Findings: Numerical analysis revealing economic impact of non-negativity wealth constraints]

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2 of 40 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.