Wenjun Zhu

• PhD FSA CERA
• Associate Professor at Nanyang Technological University

This article proposes a new copula model known as the Lévy subordinated hierarchical Archimedean copulas (LSHAC) for multicountry mortality dependence modeling. To the best of our knowledge, this is the first article to apply the LSHAC model to mortality studies. Through an extensive empirical analysis on modeling mortality experiences of 13 countr...

Determining the appropriate premium to charge for the underlying risk is central to delivering a sustainable agricultural insurance program. Though this is fundamental to all types of insurance, in agriculture this is a particularly challenging task given systemic risk, information asymmetry, and a number of multifaceted factors pertaining to the l...

We propose new neighbouring prediction models for mortality forecasting. For each mortality rate at age x in year t, denoted as mx,t, we construct images of neighbourhood mortality data around mx,t, i.e., ℇmx,t (x1, x2, s), which includes mortality information for ages in [x − x1, x + x2], lagging k years (1 ≤ k ≤ s). Combined with the deep learnin...

Weather risk affects the economy, agricultural production in particular. Index insurance is a promising tool to hedge against weather risk, but current piecewise-linear index insurance contracts face large basis risk and low demand. We propose embedding a neural network-based optimization scheme into an expected utility maximization problem to desi...

Effective agricultural insurance and risk management programs rely on accurate crop yield forecasting. In this article, a novel deep factor model for crop yield forecasting and crop insurance ratemaking is proposed. This framework first utilizes a deep autoencoder to extract a latent factor, called the production index, that integrates salient spat...

Index insurance has become a notable risk management tool in response to increasing climate variability and extreme weather events. This chapter offers a thorough review of innovative index-based financial solutions, focusing on index insurance. It explores the essential principles of index insurance, including its actuarial framework, empirical re...

We propose a new machine learning-based framework for long-term mortality forecasting. Based on ideas of neighboring prediction, model ensembling, and tree boosting, this framework can significantly improve the prediction accuracy of long-term mortality. In addition, the proposed framework addresses the challenge of a shrinking pattern in long-term...

We propose a new neighbouring prediction model for mortality forecasting. For each mortality rate at age x in year t , m x,t , we construct an image of neighbourhood mortality data around m x,t , that is, Ꜫ m x,t ( x 1 , x 2 , s ), which includes mortality information for ages in [ x - x 1 , x + x 2 ], lagging k years (1 ≤ k ≤ s ). Combined with th...

This paper provides a flexible way to address some ongoing challenges in mortality modeling, with a special focus on the mortality curvature and possible mortality plateau for extremely old ages. In particular, we extend the Gompertz law (Gompertz, 1825) by proposing a multi-factor exponential model, a framework that is able to capture flexible mor...

Accurate crop yield forecasting is central to effective risk management for many stakeholders, including farmers, insurers, and governments, in various practices, such as crop management, sales and marketing, insurance policy design, premium rate setting, and reserving. This paper first investigates an innovative approach of yield forecasting using...

Unexpected increases in life expectancy induce life insurers to extend the duration of their assets, which results in significant purchases of long-term corporate bonds. We show that this variation in life insurer demand for bonds of specific maturities has real-economy consequences for corporate sector financing and investment policies. As longevi...

Weather risk affects agricultural production. Index insurance has been proposed to hedge against severe weather risk, but large basis risk and low demand accompany current piecewise-linear index insurance contracts. We propose embedding a neural network-based optimization scheme into an expected utility maximization problem to design the index insu...

Weather index insurance is a relatively new alternative to traditional agricultural insurance such as individual yield-based crop insurance. It is still mostly at the experimental stage, rather than in widespread use like traditional crop insurance. A major challenge for weather insurance is basis risk, where the loss estimated by the index differs...

A robust predictive model for crop yield is essential for designing a commercially viable index-based insurance policy. Index-based insurance for crops is still at a relatively infant stage, and more research and development is needed in order to address a main limitation, which is referred to as basis risk. Traditionally, ground weather station me...

We contribute to the non-life experience ratemaking literature by introducing a computationally efficient approximation algorithm for the Bayesian premium in models with dynamic random effects, where the risk of a policyholder is governed by an individual process of unobserved heterogeneity. Although intuitive and flexible, the biggest challenge of...

We examine the duration-driven trades of duration-sensitive strategic investors, i.e., pensions and life insurers. We use longevity shocks as an identification strategy. Longevity shocks affect these investors' liability durations and induce them to adjust their asset durations. When the longevity shock is low (high), they buy more short-(long-) du...

The focus of this article is on predictive analytics regarding data scarcity and credibility, which are major difficulties facing the agricultural insurance sector, often due to limited loss experience data for those infrequent but extreme weather events. A new relational data matching model is presented to predict individual farmer yields in the a...

This paper provides a flexible multi-factor exponential model to address some ongoing challenges in mortality modeling, with a special focus on the mortality curvature and possible mortality plateau for extremely old ages. In particular, we extend the Gompertz law (1825) by proposing a multi-factor exponential model. The proposed framework is able...

Purpose The purpose of this paper is to propose an improved reinsurance pricing framework, which includes a crop yield forecasting model that integrates weather variables and crop production information from different geographically correlated regions using a new credibility estimator, and closed form reinsurance pricing formulas. A yield restatem...

Adverse weather-related risk is a main source of crop production loss and a big concern for agricultural insurers and reinsurers. In response, weather risk hedging may be valuable, however, due to basis risk it has been largely unsuccessful to date. This research proposes the Lévy subordinated hierarchical Archimedean copula model in modelling the...

This paper proposes a new class of premium calculation principles based on the multivariate weighted distribution, where risk loadings are imposed by transforming the density of the underlying actuarial risk by encompassing a number of external risk factors. This is a highly flexible class of premium principle with a number of desirable characteris...

The agriculture sector relies on insurance and reinsurance as a mechanism to spread loss. Possible changes in climate, such as an increase in the frequency and severity of spatially correlated weather events, may lead to increased insurance costs. In some cases the structure of risk-sharing arrangements between governments and the private sector, w...

Purpose – The purpose of this paper is to address some of the fundamental issues surrounding crop insurance ratemaking, from the perspective of the reinsurer, through the development of a scientific pricing framework. Design/methodology/approach – The generating process of the historical loss cost ratio's (LCR's) are reviewed, and the Erlang mixtu...