Optimal control problems for stochastic processes with absorbing regime

Paper: arXiv 2305.01490

Authors: yaacov Kopeliovich

Abstract

In this paper we formulate and solve an optimal problem for Stochastic process with a regime absorbing state. The solution for this problem is obtained through a system of partial differential equations. The method is applied to obtain an explicit solution for the Merton portfolio problem when an asset has a default probability in case of a log utility.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical formulation using systems of partial differential equations to solve optimal stochastic control problems with an absorbing regime, applying it to Merton’s portfolio problem under default risk. However, it is purely theoretical with virtually no empirical backtesting or real-world market data validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve optimal control for<br/>stochastic processes with absorbing regime] --> B[Inputs: Merton Portfolio Model,<br/>Default Risk & Log Utility]
    B --> C[Methodology: Formulate System of<br/>Partial Differential Equations]
    C --> D[Computation: Derive Analytical Solution<br/>for Hamilton-Jacobi-Bellman Equation]
    D --> E[Outcome: Explicit Solution for<br/>Optimal Portfolio with Asset Default Risk]