Optimal Investment with Stochastic Interest Rates and Ambiguity

ArXiv ID: 2306.13343 “View on arXiv”

Authors: Unknown

Abstract

This paper studies dynamic asset allocation with interest rate risk and several sources of ambiguity. The market consists of a risk-free asset, a zero-coupon bond (both determined by a Vasicek model), and a stock. There is ambiguity about the risk premia, the volatilities, and the correlation. The investor’s preferences display both risk aversion and ambiguity aversion. The optimal investment problem admits a closed-form solution. The solution shows that the ambiguity only affects the speculative motives of the investor, representing a hedge against the ambiguity, but not the hedging of interest rate risk. An implementation of the optimal investment strategy shows that ambiguity aversion helps to tame the highly leveraged portfolios neglecting ambiguity and leads to strategies that are more in line with popular investment advice.

Keywords: dynamic asset allocation, interest rate risk, ambiguity aversion, Vasicek model, closed-form solution

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper presents a sophisticated continuous-time stochastic control problem with multiple ambiguity sources, yielding a closed-form solution via the martingale optimality principle, indicating high mathematical density. Empirically, it includes a calibrated implementation comparing strategies with and without ambiguity, demonstrating practical portfolio behavior, though it lacks extensive backtesting or real-time data.

  flowchart TD
    A["Research Goal: Optimal Investment with Stochastic Interest Rates and Ambiguity"] --> B["Methodology: Optimal Control & HJB Equation<br/>Vasicek Model for Interest Rates"]
    B --> C["Key Inputs & Models: <br/>Risk-free Asset, Zero-coupon Bond, Stock"]
    C --> D["Computational Process: <br/>Closed-form Solution Derivation"]
    D --> E["Key Findings:<br/>1. Ambiguity affects speculative motives only<br/>2. Hedge against ambiguity (not interest rate risk)<br/>3. Reduces portfolio leverage & improves feasibility"]