Modern insurance products are becoming increasingly complex, offering various guarantees, surrender options and bonus provisions. A case in point are the with-profits insurance policies offered by UK insurers. While these policies have been offered in some form for centuries, in recent years their structure and management have become substantially more involved. The products are particularly complicated due to the wide discretion they afford insurers in determining the bonuses policyholders receive. In this paper, we study the problem of an insurance firm attempting to structure the portfolio underlying its with-profits fund. The resulting optimization problem, a non-linear program with stochastic variables, is presented in detail. Numerical results show how the model can be used to analyze the alternatives available to the insurer, such as different bonus policies and reserving methods.
Debt restructuring is one of the policy tools available for resolving sovereign debt crises and, while unorthodox, it is not uncommon. We propose a scenario analysis for debt sustainability and integrate it with scenario optimization for risk management in restructuring sovereign debt. The scenario dynamics of debt-to-GDP ratio are used to define a tail risk measure, termed conditional Debt-at-Risk. A multi-period stochastic programming model minimizes the expected cost of debt financing subject to risk limits. It provides an operational model to handle significant aspects of debt restructuring: it collects all debt issues in a common framework, and can include contingent claims, multiple currencies and step-up or linked contractual features. Alternative debt profiles – obtained by maturity rescheduling, interest payment concessions or nominal value haircuts – are analyzed for their expected cost-risk tradeoffs. With a suitable re-calculation of the efficient frontier, the risk of debt un-sustainability of alternative risk profiles can be ascertained with a given confidence level. The model is applied to Greece sovereign debt crisis analyzing the suitability of various proposals to restore debt sustainability
Simulation models of economic, financial and business risk factors are widely used to assess risks and support decision-making. Extensive literature on scenario generation methods aims at describing some underlying stochastic processes with the least number of scenarios to overcome the 'curse of dimensionality'. There is, however, an important requirement that is usually overlooked when one departs from the application domain of security pricing: the no-arbitrage condition. We formulate a moment matching model to generate multi-factor scenario trees for stochastic optimization satisfying no-arbitrage restrictions with a minimal number of scenarios and without any distributional assumptions. The resulting global optimization problem is quite general. However, it is non-convex and can grow significantly with the number of risk factors, and we develop convex lower bounding techniques for its solution exploiting the special structure of the problem. Applications to some standard problems from the literature show that this is a robust approach for tree generation. We use it to price a European basket option in complete and incomplete markets.
The sharp increase of sovereign debt internationally, since the 2008 global financial crisis, decisively contributed to several sovereign debt crises. The current COVID-19 pandemic and the fact that public debt remains high globally, have prompted a renewed interest in debt sustainability analysis (DSA) and in policy discussions concerning the most appropriate variables. We develop a normative DSA model to manage tail risk and optimize debt-financing decisions with sustainability conditions on debt stock and flow, under macroeconomic, financial, and fiscal uncertainty. We show that a risk management view alters a government’s debt-financing policy to manage tail risk better. Many uncertain variables confound the problem, and portfolio optimization using stochastic programming on scenario trees provides a versatile and effective tool to achieve sustainable debt dynamics. The model is an essential building block of the European Stability Mechanism framework to assess debt sustainability of eurozone member states, including the repayment capacity of crisis countries under €295bn assistance programs.
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