Implementing Dynamic Pricing Across Multiple Pricing Groups in Real Estate

ArXiv ID: 2411.07732 “View on arXiv”

Authors: Unknown

Abstract

This article presents a mathematical model of dynamic pricing for real estate (RE) that incorporates multiple pricing groups, thereby expanding the capabilities of existing models. The developed model solves the problem of maximizing aggregate cumulative revenue at the end of the sales period while meeting the revenue and sales goals. A method is proposed for distributing aggregate cumulative revenue goals across different RE pricing groups. The model is further modified to account for the time value of money and the real estate value increase as construction progresses. The algorithm for constructing a pricing policy for multiple pricing groups is described, and numerical simulations are performed to demonstrate how the algorithm operates.

Keywords: Dynamic Pricing, Revenue Maximization, Pricing Groups, Time Value of Money, Sales Period Optimization, Real Estate

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper presents a complex dynamic programming model with multiple pricing groups, proving optimality and deriving piecewise constant pricing policies, which constitutes advanced mathematical modeling. However, it relies solely on theoretical analysis and numerical simulations with no real-world data, backtesting, or implementation details for live trading, resulting in low empirical rigor.

  flowchart TD
    A["Research Goal:<br>Maximize Aggregate Cumulative<br>Revenue in Real Estate Sales"] --> B{"Data & Inputs"}
    B --> B1["S historic demand<br>by pricing group"]
    B --> B2["Total sales period<br>duration T"]
    B --> B3["Revenue & sales<br>goals"]

    subgraph C ["Key Methodology"]
        B --> C1["Formulate<br>Mathematical Model"]
        C1 --> C2["Distribute aggregate<br>goals across groups"]
        C2 --> C3["Modify for Time Value<br>of Money & Construction Value"]
    end

    C3 --> D{"Computational Process"}
    D --> D1["Solve Optimization<br>Algorithm"]
    D --> D2["Generate Dynamic<br>Pricing Policy"]

    D2 --> E["Key Findings / Outcomes"]
    E --> E1["Optimal pricing schedule<br>for multiple groups"]
    E --> E2["Maximized cumulative<br>revenue"]
    E --> E3["Met sales & revenue<br>goals within period"]
    E --> E4["Numerical simulations<br>validate algorithm"]