Private Equity Valuation with Quadratic Utility: A Continuous-Time Framework

Written By Chris Smith

ADIA Lab Research Paper Series

Authors: Alexander Lipton, Marcos López del Prado

Date Published: September 2025

This chapter presents a new approach to valuing private equity (PE) investments by developing analytical methods tailored to investors with quadratic utility preferences. It provides explicit solutions to the nonlinear partial di¤erential equations that describe the certainty (equivalent value of these investments) equations that arise from a two-dimensional Hamilton-Jacobi-Bellman (HJB) framework. The results take into account key features of private equity, including illiquidity, market incompleteness, and nonlinear dynamics. The chapter also includes several practical examples and calculates the optimal way to divide capital between liquid and illiquid assets.

DOWNLOAD THIS PAPER
Chris Smith
Previous

Rethinking Portfolio Risk: A Taxonomy for Asset Management
Next

From Apophatic Interpretability to Accountable Explainability: A Layered Governance Architecture for Structural Opacity in Explainable AI