Pricing catastrophe bonds with multistage stochastic programming

An increasing number of practical scenarios continue to experience problems associated with multistage stochastic programming. This study proposes a decomposition method through which they can be a successful solution to multi-stage stochastic nonlinear programs. The proposed method entails the scenario analysis method. The proposed method also performs its role via search direction generation in such a way that sets of quadratic programming sub-issues are solved in a parallel way, especially when the size is significant lower, compared to the case involving original problems at the respective iterations. Relative to the dual multiplier derivation, which focuses on non-anticipativity constraints, the proposed system advocates for the introduction of generalized reduced gradient approaches.

Contributors

To encourage further development of catastrophe (cat) bond, understanding the causes of cat bond premium puzzle is necessitated. Considering the property of entropy to measure uncertainty, this paper establishes an entropy model about risk assessment in catastrophe bond investors' decision making. Moreover, this article analyzes the model and compares relative influence through simulating actual behavior of both rational and non-rational investors. The conclusions obtained show that with inadequate information, cognitive biases and collecting cost increase the high yield demand of investors in cat bond market.

This study focuses on a multi-product, multi-period, multi-site supply chain planning problem under demand uncertainty. A multi-stage stochastic linear programming model is proposed to maximize the expected profit. The decisions to be made comprise the production amount, the inventory and backorder sizes as well as the quantity of products to be transported between upstream and downstream plants and customers in each period. A numerical example is presented in order to illustrate the effectiveness of the proposed model. Results indicate that the solution of the multi-stage stochastic model outperforms the deterministic and the two-stage stochastic models.

Practical planning problems with deterministic forecasts of inherently uncertain parameters often yield unsatisfactory solutions. Stochastic programming formulations allow uncertain parameters to be modeled as random variables with known distributions, but the size of the resulting mathematical programs can be formidable. Decomposition-based algorithms take advantage of special structure and provide an attractive approach to such problems. We consider two classes of decomposition-based stochastic programming algorithms. The first type of algorithm addresses problems with a ``manageable`` number of scenarios. The second class incorporates Monte Carlo sampling within a decomposition algorithm. We develop and empirically study an enhanced Benders decomposition algorithm for solving multistage stochastic linear programs within a prespecified tolerance. The enhancements include warm start basis selection, preliminary cut generation, the multicut procedure, and decision tree traversing strategies. Computational results are presented for a collection of ``real-world`` multistage stochastic hydroelectric scheduling problems. Recently, there has been an increased focus on decomposition-based algorithms that use sampling within the optimization framework. These approaches hold much promise for solving stochastic programs with many scenarios. A critical component of such algorithms is a stopping criterion to ensure the quality of the solution. With this as motivation, we develop a stopping rule theory for algorithms in which bounds on the optimal objective function value are estimated by sampling. Rules are provided for selecting sample sizes and terminating the algorithm under which asymptotic validity of confidence interval statements for the quality of the proposed solution can be verified. Issues associated with the application of this theory to two sampling-based algorithms are considered, and preliminary empirical coverage results are presented.

Insurance securitization has long been hailed as an important tool to increase the underwriting capacity for companies exposed to catastrophe-related risks. However, global volumes of insurance securitization have remained surprisingly low to date which raises questions over its benefits. In this paper, we examine changes in the market value of insurance and reinsurance firms which announce their engagement in insurance securitization by issuing catastrophe (Cat) bonds. Consistent with the hitherto underwhelming contribution of Cat bonds to global catastrophe coverage, we do not find evidence that Cat bonds lead to strong wealth gains for shareholders in the issuing firm. More importantly, we report large variations in the distribution of wealth effects in response to the issue announcement. We show that the wealth effects for shareholders in firms which issue Cat bonds appear to be driven by explanations according to which Cat bonds offer cost savings relative to other forms of catastrophe risk management (and less by the potential of Cat bonds to hedge catastrophe risk). Thus, abnormal returns are particularly large for issues by firms which face low levels of loss uncertainty (which reduces the information acquisition costs in financial markets) as well as for issues during periods when prices for catastrophe coverage (including Cat bonds) are low.

Common Risk Factors in the Cross Section of Catastrophe Bond Returns

Multistage stochastic programming problems well correspond to many practical situations in which a random element exists and moreover it is reasonable to treat them with respect to some discrete time interval. In particular, this type of problems correspond to practical situations that can be considered with respect to some time interval and simultanously decomposed with respect to the individual time points. The aim of this paper is to investigate the objective functions corresponding to the individual problems belonging to the one multistage stochastic programming problem. A special attention is paid to the Lipschitz property.

To address the uncertain renewable energy in the day-ahead optimal dispatch of energy and reserve, a multi-stage stochastic programming model is established in this paper to minimize the expected total costs. The uncertainties over the multiple stages are characterized by a scenario tree and the optimal dispatch scheme is cast as a decision tree which guarantees the flexibility to decide the reasonable outputs of generation and the adequate reserves accounting for different realizations of renewable energy. Most importantly, to deal with the “Curse of Dimensionality” of stochastic programming, stochastic dual dynamic programming (SDDP) is employed, which decomposes the original problem into several sub-problems according to the stages. Specifically, the SDDP algorithm performs forward pass and backward pass repeatedly until the convergence criterion is satisfied. At each iteration, the original problem is approximated by creating a linear piecewise function. Besides, an improved convergence criterion is adopted to narrow the optimization gaps. The results on the IEEE 118-bus system and real-life provincial power grid show the effectiveness of the proposed model and method.

Multistage stochastic programs have applications in many areas and support policy makers in finding rational decisions that hedge against unforeseen negative events. In order to ensure computational tractability, continuous-state stochastic programs are usually discretized; and frequently, the curse of dimensionality dictates that decision stages must be aggregated. In this article we construct two discrete, stage-aggregated stochastic programs which provide upper and lower bounds on the optimal value of the original problem. The approximate problems involve finitely many decisions and constraints, thus principally allowing for numerical solution.

The purpose of this paper is to apply multistage stochastic programming to the transmission line expansion planning problem, especially when uncertain demand scenarios exist. Since the problem of transmission line expansion planning requires an intensive computational load, dual decomposition is used to decompose the problem into smaller problems. Following this, progressive hedging and proximal bundle methods are used to restore the decomposed solutions to the original problems. Mixed-integer linear programming is involved in the problem to decide where new transmission lines should be constructed or reinforced. However, integer variables in multistage stochastic programming (MSSP) are intractable since integer variables are not restored. Therefore, the branch-and-bound algorithm is applied to multistage stochastic programming methods to force convergence of integer variables.In addition, this paper suggests combining progressive hedging and dual decomposition in stochastic integer programming by sharing penalty parameters. The simulation results tested on the IEEE 30-bus system verify that our combined model sped up the computation and achieved higher accuracy by achieving the minimised cost.

The HuT (The Human-Tech Nexus) project, funded by Horizon Europe initiative, is focused on risk assessment and disaster risk reduction for distinct types of hazards (wildfires, landslide, droughts, etc.), over the European territory, by means of a series of demonstrators representing a multi-hazard arena. In the framework of this project, we present an innovative Catastrophe Bond (Cat Bond) designed to enhance disaster risk reduction strategies. Cat Bonds are a key financial instrument for transferring the risk of extreme events from insurers to capital markets, thereby increasing resilience and reducing the economic impact of disasters. Our approach lies in the use of the recently developed E3CI (European Extreme Events Climate Index) as the trigger mechanism for the bond. The E3CI is a suite of indicators designed to monitor and quantify the occurrence and intensity of climate extremes across Europe. It integrates multiple variables into a single, scientifically robust metric, enabling consistent and transparent assessment of climate-related risks. By using E3CI as the trigger for our Cat Bond, we ensure that payouts are based on objective, observed climate conditions rather than loss estimates, improving reliability and fairness in risk transfer mechanisms. The coupon here reckoned for the Cat Bond are based on hypothetical portfolios over the Italian territory. The proposed Cat Bond ensures transparency, objectivity, and a strong link to observed climate extremes. This solution represents an interesting case study in integrating climate science into risk financing solutions, supporting both insurers and communities in managing the growing risks associated with climate change.

Analysis of Risk Premium Determinants on Cat Bonds

The study of natural catastrophe models plays an important role in the prevention and mitigation of disasters. After the occurrence of a natural disaster, the reconstruction can be financed with catastrophe bonds (CAT bonds) or reinsurance. This paper examines the calibration of a real parametric CAT bond for earthquakes that was sponsored by the Mexican government, which is based on the estimation of the intensity rate of the arrival process of earthquake (which would trigger this particular CAT bond) from the two sides of the contract: the reinsurance and the capital markets. Additionally, the intensity rate from the historical data was estimated to conduct a comparative analysis. The results demonstrate that, under specific conditions, the financial strategy of the government, a mix of reinsurance and CAT bond, is optimal in the sense that it provides coverage of USD 450 million for a lower cost than the reinsurance itself. <italic>JEL Classification: G19, G29, N26, N56, Q29, Q54</italic>

Multistage stochastic programming (SP) with both endogenous and exogenous uncertainties is a novel problem in which some uncertain parameters are decision-dependent and others are independent of decisions. The main difficulty of this problem is that nonanticipativity constraints (NACs) make up a significantly large constraint set, growing very fast with the number of scenarios and leading to an intractable model. Usually, a lot of these constraints are redundant and hence, identification and elimination of redundant NACs can cause a significant reduction in the problem size. Recently, a polynomial time algorithm has been proposed in the literature which is able to identify all redundant NACs in an SP problem with only endogenous uncertainty. In this paper, however, we extend the algorithm proposed in the literature and present a new method which is able to make the upper most possible reduction in the number of NACs in any SP with both exogenous and endogenous uncertain parameters. Proving the validity of this method is another innovation of this study. Computational results confirm that the proposed approach can significantly reduce the problem size within a reasonable computation time.