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Financial Risk Management Best Practice

Optimal Long-Term Property and Casualty ALM with Risk Capital Control

by Giorgio Consigli and Massimo di Tria

This Chapter Covers1

  • P&C strategic planning under liability constraints.

  • Short-term profitability and long-term sustainability.

  • Economic risk capital control.

  • An optimization framework for long-term property and casualty ALM.


Increasing competition and record property and casualty (P&C) insurance claims reported by global players in recent years (Comité Européen des Assurances, 2010) have generated remarkable pressure on the financial stability of P&C divisions within insurance firms, leading to increased technical reserves and higher capital requirements. At the same time investment management divisions have expanded, reinforcing the role of insurers as institutional investors competing in fixed-income and equity markets with other players, such as pension and mutual funds. Furthermore, the Solvency II regulatory agreement (see European Parliament, 2009) is currently forcing an historic change toward risk-based capital allocation measures for insurance companies as a whole.

In this context, a strong operational incentive has facilitated the integration of the historical insurance business with the investment management business. Such integration is also motivated by the perceived role of the P&C division as a liquidity buffer generated by fixed-income portfolios that are typically held by risk-averse investment divisions.

In this chapter we clarify the complex interaction between the operational constraints of the investment and insurance functions, which motivates a strategy based on short-term profit targets and longer-term risk-adjusted return goals. From a mathematical viewpoint, the problem finds a natural formulation as a dynamic stochastic program (DSP) (Ziemba and Mulvey, 1998; Zenios and Ziemba, 2007; Bertocchi, Consigli, and Dempster, 2011) that integrates a realistic representation of the asset–liability management (ALM) problem with an uncertainty model which captures insurance and investment risks. Contrary to current standards in insurance-based investment divisions, which rely largely on one-period static approaches, the adoption of a dynamic approach allows both the extension of the decision horizon and a more accurate short-term modeling of P&C variables.

One-period, static decision models are typically based on a one-year horizon, with estimates of premiums, casualty reserves, and all relevant P&C liabilities, as well as financial market scenarios, all projected at the one-year horizon. The markets’ dynamics generate the risk that the investment manager is required to monitor over time. In a static model, end-of-year goals typically focus on the achievement of an operating profit that captures both the company’s technical activity and its investment policy.

The neglect of the time beyond the end of the current accounting year may, however, severely affect the likelihood of achieving investment goals at the three-year industrial plan horizon. At a longer, 10-year horizon an additional decision criterion may be considered to take into account the company’s overall risk exposure and its long-term business sustainability.

In this chapter we summarize the key elements of an asset–liability management problem, integrating the definition of an optimal asset allocation policy over a 10-year planning horizon with the inclusion of liability constraints generated by an ongoing P&C business (Consigli et al., 2011; Mulvey and Erkan, 2005). The investment universe includes fixed-income and equity asset classes as well as real estate and alternative investments. The results come from a representative, real-world case problem, developed for a global P&C insurance company. As for many other global players in the market, the insurance company for which the model has been developed has a historic record of liability-driven strategic asset allocation that largely relies on sophisticated statistical models and simulation tools, as well as one-period optimization techniques.

Dynamic stochastic programming techniques have only occasionally been applied to ALM problems for the insurance sector since the seminal work by Cariño et al. (1994; see also Zenios and Ziemba, 2007) for the Japanese Yasuda Kasai Insurance Company. A notable example, which specifically addresses a strategic management problem for P&C insurance through stochastic programming approaches, is given by Mulvey and Erkan (2005) for the US market in particular. Far more extensive is the related literature on institutional ALM problems, which have similar features to the analysis presented here (Ziemba and Mulvey, 1998; Bertocchi, Consigli, and Dempster, 2011).

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Further reading


  • Bertocchi, Marida Ida, Giorgio Consigli, and Michael A. H. Dempster (eds). Stochastic Optimization Methods in Finance and Energy: New Financial Products and Energy Market Strategies. New York, etc.: Springer, 2011.
  • Pflug, Georg Ch., and Werner Romisch. Modeling, Measuring and Managing Risk. Singapore: World Scientific Publishing, 2007.
  • Zenios, Stavros A., and William T. Ziemba (eds). Handbook of Asset and Liability Management. Volume 1: Theory and Methodology. Amsterdam: Elsevier, 2007a.
  • Zenios, Stavros A., and William T. Ziemba (eds). Handbook of Asset and Liability Management. Volume 2: Applications and Case Studies. Amsterdam: Elsevier, 2007b.
  • Ziemba, William T., and John M. Mulvey (eds). Worldwide Asset and Liability Modeling. Cambridge, UK: Cambridge University Press, 1998.


  • Cariño, David R., Terry Kent, David H. Myers, Celine Stacy, Mike Sylvanus, Andrew L. Turner, Kouji Watanabe, and William T. Ziemba. “The Russell–Yasuda Kasai model: An asset/liability model for a Japanese insurance company using multistage stochastic programming.” Interfaces 24:1 (1994): 29–49.
  • Comité Européen des Assurances (CEA). “CEA statistics no. 42: European insurance in figures.” Brussels: CEA, November 2010. Online at:
  • Consigli, Giorgio, Massimo di Tria, Michele Gaffo, Gaetano Iaquinta, Vittorio Moriggia, and Angelo Uristani. “Dynamic portfolio management for property and casualty insurance.” In Bertocchi, Consigli, and Dempster (eds), Stochastic Optimization Methods in Finance and Energy: New Financial Products and Energy Market Strategies, Springer, 2011, pp. 99–124.
  • Europe Economics. “Retail insurance market study MARKT/2008/18/H. Final report by Europe Economics.” London, UK: November 2009. Online at:
  • European Parliament. “Directive 2009/138/EC of the European Parliament and of the Council of 25 November 2009 on the taking-up and pursuit of the business of insurance and reinsurance (Solvency II) (recast).” Official Journal of the European Union L335/1, December 17, 2009. Online at:
  • Mulvey, John M., and Hafize Gaye Erkan. “Decentralized risk management for global property and casualty insurance companies.” In Stein W. Wallace and William T. Ziemba (eds), Applications of Stochastic Programming, Philadelphia, PA: Society for Industrial and Applied Mathematics and the Mathematical Programming Society, 2005, pp. 503–530.

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