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Insurance Portfolio Valuation under Market Jumps: A Framework Combining Kou Jump-Diffusion Forecasting and Dynamic CPPI Hedging

Jurnal Matematika, Statistika dan Komputasi · Vol. 23 No. 1 (2026) · pp. 7–19

DOI
10.20956/gxed0068
ISSN
2614-8811, 1858-1382
Published
2026-09-15
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

This study develops an integrated valuation framework for insurance portfolios under discontinuous market conditions. The framework combines asset-price forecasting based on the Kou jump-diffusion model with Dynamic Constant Proportion Portfolio Insurance (D-CPPI) to support portfolio protection and capital guarantee management. The Kou jump-diffusion model is employed to capture asymmetric jumps and extreme market movements, while D-CPPI dynamically allocates wealth between risky and risk-free assets. To address gap risk, a volatility-adjusted risk multiplier with a non-negativity constraint is incorporated into the portfolio insurance mechanism. The proposed framework is evaluated using S&P 500 index data from 2006–2010 at daily, weekly, and monthly observation frequencies. The forecasting results demonstrate satisfactory predictive performance, with Mean Absolute Percentage Error (MAPE) values of 4.76%, 5.04%, and 5.36% for the daily, weekly, and monthly models, respectively. Portfolio simulations indicate that arbitrarily selected multipliers can lead to substantial losses and floor violations, whereas the constrained volatility-adjusted multiplier maintains portfolio values above the guaranteed floor across all observation frequencies and effectively mitigates gap risk. These findings suggest that integrating Kou jump-diffusion forecasting with D-CPPI provides an effective approach for insurance portfolio valuation under volatile market conditions. The proposed framework contributes to the literature by jointly addressing asset-price jumps, dynamic portfolio allocation, and gap-risk mitigation within a unified insurance portfolio management framework.

Keywords

Collaboration network of the authors

18 authors · 31 co-authorship links

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

  • Politeknik Negeri Ujung Pandang
  • Bandung Institute of Technology
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Nurhayati NurhayatiPoliteknik Negeri Ujung Pandang2
Utriweni MukhaiyarAffiliation unknown2
Muhammad Rozzaq HamidiAffiliation unknown2
Jova Edri SaputraAffiliation unknown2
Randi DeautamaAffiliation unknown1
Ady FebrisutisyantoAffiliation unknown1
I Gusti Ayu Wulan AnggasariAffiliation unknown1
Ahmad Fuad ZainuddinAffiliation unknown1
Muhammad Haekal YunusAffiliation unknown1
Firman AdiyansyahAffiliation unknown1
Steven SergioAffiliation unknown1
Enrico AntoniusAffiliation unknown1
Udjianna Sekteria PasaribuBandung Institute of Technology1
Adilan Widyawan MahdiyasaAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">Insurance Portfolio Valuation under Market Jumps: A Framework Combining Kou Jump-Diffusion Forecasting and Dynamic CPPI Hedging </dc:title>
	<dc:creator xml:lang="en">Fitriawati, Andi</dc:creator>
	<dc:creator xml:lang="en">Indratno, Sapto Wahyu</dc:creator>
	<dc:creator xml:lang="en">Sari, Kurnia Novita</dc:creator>
	<dc:creator xml:lang="en">Febrianti, Werry</dc:creator>
	<dc:subject xml:lang="en">Dynamic-CPPI</dc:subject>
	<dc:subject xml:lang="en">Hedging</dc:subject>
	<dc:subject xml:lang="en">Kou jump difussion</dc:subject>
	<dc:subject xml:lang="en">Unit-linked portfolio valuation</dc:subject>
	<dc:subject xml:lang="en">Actuarial Science</dc:subject>
	<dc:subject xml:lang="en">Financial Modeling</dc:subject>
	<dc:subject xml:lang="en">Portfolio</dc:subject>
	<dc:subject xml:lang="en">Insurance Mathematics</dc:subject>
	<dc:subject xml:lang="en">Risk Management</dc:subject>
	<dc:subject xml:lang="en">Stochastic Interest Rate</dc:subject>
	<dc:description xml:lang="en">This study develops an integrated valuation framework for insurance portfolios under discontinuous market conditions. The framework combines asset-price forecasting based on the Kou jump-diffusion model with Dynamic Constant Proportion Portfolio Insurance (D-CPPI) to support portfolio protection and capital guarantee management. The Kou jump-diffusion model is employed to capture asymmetric jumps and extreme market movements, while D-CPPI dynamically allocates wealth between risky and risk-free assets. To address gap risk, a volatility-adjusted risk multiplier with a non-negativity constraint is incorporated into the portfolio insurance mechanism. The proposed framework is evaluated using S&amp;amp;P 500 index data from 2006–2010 at daily, weekly, and monthly observation frequencies. The forecasting results demonstrate satisfactory predictive performance, with Mean Absolute Percentage Error (MAPE) values of 4.76%, 5.04%, and 5.36% for the daily, weekly, and monthly models, respectively. Portfolio simulations indicate that arbitrarily selected multipliers can lead to substantial losses and floor violations, whereas the constrained volatility-adjusted multiplier maintains portfolio values above the guaranteed floor across all observation frequencies and effectively mitigates gap risk. These findings suggest that integrating Kou jump-diffusion forecasting with D-CPPI provides an effective approach for insurance portfolio valuation under volatile market conditions. The proposed framework contributes to the literature by jointly addressing asset-price jumps, dynamic portfolio allocation, and gap-risk mitigation within a unified insurance portfolio management framework.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2026-09-15</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:type xml:lang="en">Text</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/49589</dc:identifier>
	<dc:identifier>10.20956/gxed0068</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 23 No. 1 (2026): September 2026; 7-19</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/49589/15001</dc:relation>
	<dc:coverage xml:lang="en">Actuarial science and financial mathematics applications in unit-linked insurance portfolios using jump diffusion and CPPI hedging.</dc:coverage>
	<dc:rights xml:lang="en">Copyright (c) 2026 Jurnal Matematika, Statistika dan Komputasi</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
</oai_dc:dc>