Optimal Cash Transfers and Microinsurance to Reduce Social Protection Costs

Paper: arXiv 2511.07431

Authors: Pablo Azcue, Corina Constantinescu, José Miguel Flores-Contró, Nora Muler

Abstract

Design and implementation of appropriate social protection strategies is one of the main targets of the United Nation’s Sustainable Development Goal (SDG) 1: No Poverty. Cash transfer (CT) programmes are considered one of the main social protection strategies and an instrument for achieving SDG 1. Targeting consists of establishing eligibility criteria for beneficiaries of CT programmes. In low-income countries, where resources are limited, proper targeting of CTs is essential for an efficient use of resources. Given the growing importance of microinsurance as a complementary tool to social protection strategies, this study examines its role as a supplement to CT programmes. In this article, we adopt the piecewise-deterministic Markov process introduced in Kovacevic and Pflug (2011) to model the capital of a household, which when exposed to proportional capital losses (in contrast to the classical Cramér-Lundberg model) can push them into the poverty area. Striving for cost-effective CT programmes, we optimise the expected discounted cost of keeping the household’s capital above the poverty line by means of injection of capital (as a direct capital transfer). Using dynamic programming techniques, we derive the Hamilton-Jacobi-Bellman (HJB) equation associated with the optimal control problem of determining the amount of capital to inject over time. We show that this equation admits a viscosity solution that can be approximated numerically. Moreover, in certain special cases, we obtain closed-form expressions for the solution. Numerical examples show that there is an optimal level of injection above the poverty threshold, suggesting that efficient use of resources is achieved when CTs are preventive rather than reactive, since injecting capital into households when their capital levels are above the poverty line is less costly than to do so only when it falls below the threshold.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical formulation using piecewise-deterministic Markov processes, stochastic optimal control, and HJB equations with viscosity solutions. However, it is purely theoretical and lacks empirical backtesting or real-world dataset validation, relying only on stylized numerical examples.

Research Flowchart

  flowchart TD
    A[Goal: Minimize Social Protection Costs via Optimal Cash Transfers & Microinsurance] --> B[Model Household Capital as Piecewise-Deterministic Markov Process]
    B --> C[Formulate Optimal Control Problem to Keep Capital Above Poverty Line]
    C --> D[Derive Hamilton-Jacobi-Bellman Equation & Prove Viscosity Solution]
    D --> E[Solve HJB Equation via Closed-Form Expressions & Numerical Approximations]
    E --> F[Finding: Preventive CTs Above Poverty Line Are More Cost-Effective Than Reactive CTs]

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0 of 41 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.