Benjamin Avanzi

Benjamin Avanzi
University of Melbourne | MSD · Department of Economics

PhD
Professor of Actuarial Studies at the University of Melbourne

About

84
Publications
9,247
Reads
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882
Citations
Additional affiliations
February 2020 - present
University of Melbourne
Position
  • Professor
June 2015 - May 2018
Université de Montréal
Position
  • Professor (Associate)
May 2015 - January 2020
UNSW Sydney
Position
  • Professor (Associate)

Publications

Publications (84)
Preprint
Optimal reinsurance is a perennial problem in insurance. The problem formulation considered in this paper is closely connected to the optimal portfolio problem in finance, with some important distinctions. In particular, the surplus of an insurance company is routinely approximated by a Brownian motion, as opposed to the geometric Brownian motion u...
Article
In recent years, new techniques based on artificial intelligence and machine learning in particular have been making a revolution in the work of actuaries, including in loss reserving. A particularly promising technique is that of neural networks, which have been shown to offer a versatile, flexible and accurate approach to loss reserving. However,...
Preprint
In this paper, we first introduce a simulator of cases estimates of incurred losses, called `SPLICE` (Synthetic Paid Loss and Incurred Cost Experience). In three modules, case estimates are simulated in continuous time, and a record is output for each individual claim. Revisions for the case estimates are also simulated as a sequence over the lifet...
Article
In this paper, we model the cash surplus (or equity) of a risky business with a Brownian motion (with a drift). Owners can take cash out of the surplus in the form of “dividends”, subject to transaction costs. However, if the surplus hits 0 then ruin occurs and the business cannot operate any more. We consider two types of dividend distributions: (...
Article
The Markov-modulated Poisson process is utilised for count modelling in a variety of areas such as queueing, reliability, network and insurance claims analysis. In this paper, we extend the Markov-modulated Poisson process framework through the introduction of a flexible frequency perturbation measure. This contribution enables known information of...
Preprint
Loss reserving generally focuses on identifying a single model that can generate superior predictive performance. However, different loss reserving models specialise in capturing different aspects of loss data. This is recognised in practice in the sense that results from different models are often considered, and sometimes combined. For instance,...
Article
In this paper, we first introduce a simulator of cases estimates of incurred losses called SPLICE ( S ynthetic P aid L oss and I ncurred C ost E xperience). In three modules, case estimates are simulated in continuous time, and a record is output for each individual claim. Revisions for the case estimates are also simulated as a sequence over the l...
Preprint
In this paper we consider a company whose assets and liabilities evolve according to a correlated bivariate geometric Brownian motion, such as in Gerber and Shiu (2003). We determine what dividend strategy maximises the expected present value of dividends until ruin in two cases: (i) when shareholders won't cover surplus shortfalls and a solvency c...
Preprint
Traditional techniques for calculating outstanding claim liabilities such as the chain ladder are notoriously at risk of being distorted by outliers in past claims data. Unfortunately, the literature in robust methods of reserving is scant, with notable exceptions such as Verdonck and Debruyne (2011) and Verdonck and Van Wouwe (2011). In this paper...
Preprint
The sensitivity of loss reserving techniques to outliers in the data or deviations from model assumptions is a well known challenge. It has been shown that the popular chain-ladder reserving approach is at significant risk to such aberrant observations in that reserve estimates can be significantly shifted in the presence of even one outlier. As a...
Preprint
Neural networks offer a versatile, flexible and accurate approach to loss reserving. However, such applications have focused primarily on the (important) problem of fitting accurate central estimates of the outstanding claims. In practice, properties regarding the variability of outstanding claims are equally important (e.g., quantiles for regulato...
Article
Recent years have seen rapid increase in the application of machine learning to insurance loss reserving. They yield most value when applied to large data sets, such as individual claims, or large claim triangles. In short, they are likely to be useful in the analysis of any data set whose volume is sufficient to obscure a naked-eye view of its fea...
Article
Maximising dividends is one classical stability criterion in actuarial risk theory. Motivated by the fact that dividends are paid periodically in real life, periodic dividend strategies were recently introduced (Albrecher et al. 2011). In this paper, we incorporate fixed transaction costs into the model and study the optimal periodic dividend strat...
Article
In this paper, we develop a method to model and estimate several, dependent count processes, using granular data. Specifically, we develop a multivariate Cox process with shot noise intensities to jointly model the arrival process of counts (e.g. insurance claims). The dependency structure is introduced via multivariate shot noise intensity process...
Article
Full-text available
The classical Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of n mutually independent and identically distributed random variables with finite second moment converges in distribution to a standard Gaussian as n goes to infinity. In particular, pairwise ind...
Preprint
Full-text available
A simulator of individual claim experience called SynthETIC is described. It is publicly available, open source and fills a gap in the non-life actuarial toolkit. It simulates, for each claim, occurrence, notification, the timing and magnitude of individual partial payments, and closure. Inflation, including (optionally) superimposed inflation, is...
Article
Introducing common shocks is a popular dependence modelling approach, with some recent applications in loss reserving. The main advantage of this approach is the ability to capture structural dependence coming from known relationships. In addition, it helps with the parsimonious construction of correlation matrices of large dimensions. However, com...
Preprint
Full-text available
In this paper, we model the cash surplus (or equity) of a risky business with a Brownian motion. Owners can take cash out of the surplus in the form of ``dividends'', subject to transaction costs. However, if the surplus hits 0 then ruin occurs and the business cannot operate any more. We consider two types of dividend distributions: (i) periodic,...
Article
We consider the general class of spectrally positive Lévy risk processes, which are appropriate for businesses with continuous expenses and lump sum gains whose timing and sizes are stochastic. Motivated by the fact that dividends cannot be paid at any time in real life, we study periodic dividend strategies whereby dividend decisions are made acco...
Preprint
Full-text available
Introducing common shocks is a popular dependence modelling approach, with some recent applications in loss reserving. The main advantage of this approach is the ability to capture structural dependence coming from known relationships. In addition, it helps with the parsimonious construction of correlation matrices of large dimensions. However, com...
Preprint
Full-text available
In this paper, we focus on estimating ultimate claim counts in multiple insurance processes and thus extend the associated literature of micro-level stochastic reserving models to the multivariate context. Specifically, we develop a multivariate Cox process to model the joint arrival process of insurance claims in multiple Lines of Business. The de...
Preprint
In this paper, we develop a multivariate evolutionary generalised linear model (GLM) framework for claims reserving, which allows for dynamic features of claims activity in conjunction with dependency across business lines to accurately assess claims reserves. We extend the traditional GLM reserving framework on two fronts: GLM fixed factors are al...
Preprint
Full-text available
Maximising dividends is one classical stability criterion in actuarial risk theory. Motivated by the fact that dividends are paid periodically in real life, $\textit{periodic}$ dividend strategies were recently introduced (Albrecher, Gerber and Shiu, 2011). In this paper, we incorporate fixed transaction costs into the model and study the optimal p...
Article
In this paper, we develop a multivariate evolutionary generalised linear model (GLM) framework for claims reserving, which allows for dynamic features of claims activity in conjunction with dependency across business lines to accurately assess claims reserves. We extend the traditional GLM reserving framework on two fronts: GLM fixed factors are al...
Preprint
Full-text available
We consider the general class of spectrally positive L\'evy risk processes, which are appropriate for businesses with continuous expenses and lump sum gains whose timing and sizes are stochastic. Motivated by the fact that dividends cannot be paid at any time in real life, we study $\textit{periodic}$ dividend strategies whereby dividend decisions...
Preprint
Full-text available
The Markov-modulated Poisson process is utilised for count modelling in a variety of areas such as queueing, reliability, network and insurance claims analysis. In this paper, we extend the Markov-modulated Poisson process framework through the introduction of a flexible frequency perturbation measure. This contribution enables known information of...
Preprint
Full-text available
The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of n mutually independent and identically distributed random variables with finite first and second moments converges in distribution to a standard Gaussian as n goes to infinity. In particular, pairwise in...
Preprint
Full-text available
The Central Limit Theorem (CLT) is one of the most fundamental results in Statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and second moments converges in distribution to a standard Gaussian as $n$ goes to infinity. In particular, pairwis...
Article
The paper is concerned with multiple claim arrays. In recognition of the extensive use by practitioners of large correlation matrices for the estimation of diversification benefits in capital modelling, we develop a methodology for the construction of such correlation structures (to any dimension). Indeed, the literature does not document any metho...
Article
We consider a profitable, risky setting with two separate, correlated asset and liability processes (first introduced by Gerber and Shiu, 2003). The company that is considered is allowed to distribute excess profits (traditionally referred to as dividends in the literature), but is regulated and is subject to particular regulatory (solvency) constr...
Article
In the classical dividends problem, dividend decisions are allowed to be made at any time. Under such a framework, the optimal dividend strategies are often of barrier or threshold type, which can lead to very irregular dividend payments over time. In practice however companies distribute dividends on a periodic basis. In that spirit, “Erlangisatio...
Article
The expected present value of dividends is one of the classical stability criteria in actuarial risk theory. In this context, numerous papers considered threshold (refractive) and barrier (reflective) dividend strategies. These were shown to be optimal in a number of different contexts for bounded and unbounded payout rates, respectively. In this p...
Article
Stochastic loss reserving with dependence has received increased attention in the last decade. A number of parametric multivariate approaches have been developed to capture dependence between lines of business within an insurer’s portfolio. Motivated by the richness of the Tweedie family of distributions, we propose a multivariate Tweedie approach...
Working Paper
Full-text available
The expected present value of dividends is one of the classical stability criteria in actuarial risk theory. In this context, numerous papers considered threshold (refractive) and barrier (reflective) dividend strategies. These were shown to be optimal in a number of different contexts for bounded and unbounded payout rates, respectively. In this p...
Article
The accurate estimation of outstanding liabilities of an insurance company is an essential task. This is to meet regulatory requirements, but also to achieve efficient internal capital management. Over the recent years, there has been increasing interest in the utilisation of insurance data at a more granular level, and to model claims using stocha...
Article
In the classical optimal dividends problem, dividend decisions are allowed to be made at any point in time — according to a continuous strategy. Depending on the surplus process that is considered and whether dividend payouts are bounded or not, optimal strategies are generally of a band, barrier or threshold type. In reality, while surpluses chang...
Article
The paper is concerned with multiple claim arrays. We construct a broad and flexible family of models, where dependency is induced by common shock components. Models incorporate dependencies between observations both within arrays and between arrays. Arrays are of general shape (possibly with holes), but include the usual cases of claim triangles a...
Article
In this paper, we consider a profitable, risky setting with two separate, correlated asset and liability processes (first introduced by Gerber and Shiu, 2003). The company that is considered is allowed to distribute excess profits (traditionally referred to as dividends in the literature), but is regulated and is subject to particular regulatory (s...
Technical Report
The accurate estimation of outstanding liabilities of an insurance company is an essential task. This is to meet regulatory requirements, but also to achieve efficient internal capital management. Over the recent years, there has been increasing interest in the utilisation of insurance data at a more granular level, and to model claims using stocha...
Article
Full-text available
Because of the profitable nature of risk businesses in the long term, de Finetti (1957) suggested that surplus models should allow for cash leakages, as otherwise the surplus would unrealistically grow (on average) to the infinity. These leakages were interpreted as 'dividends'. Subsequent literature on actuarial surplus models with dividend distri...
Research
Full-text available
In the classical optimal dividends problem, dividend decisions are allowed to be made at any point in time - according to a continuous strategy. Depending on the surplus process that is considered and whether dividend payouts are bounded or not, optimal strategies are generally of a band, barrier, or threshold type. In reality, while surpluses chan...
Research
Full-text available
In this paper, we bootstrap data on Canadian pensioners’ mortality (spanning 1999–2008) that was recently published by the Canadian Institute of Actuaries (2014) in order to study the characteristics of its implied heterogeneity. We find strong support for the gamma frailty model. It is remarkable that our results are obtained without making any di...
Article
Full-text available
This paper is concerned with dependency between business segments in the Property & Casualty industry. When considering the business of an insurance company at the aggregate level, dependence structures can have a major impact in several areas of Enterprise Risk Management, such as in claims reserving and capital modelling. The accurate estimation...
Article
Because of the profitable nature of risk businesses in the long term, de Finetti suggested that surplus models should allow for cash leakages, as otherwise the surplus would unrealistically grow (on average) to infinity. These leakages were interpreted as ‘dividends’. Subsequent literature on actuarial surplus models with dividend distribution has...
Article
Full-text available
We develop a generalisation of the World Bank (1994) model of forced saving for retirement. This broader model consists of two tiers of second pillar savings – mandated and non-mandated (voluntary). Furthermore, the government can set two types of guarantees on the first (mandated) tier – investment returns and annuity prices – leading to possible...
Article
The dual model with diffusion is appropriate for companies with continuous expenses that are offset by stochastic and irregular gains. Examples include research-based or commission-based companies. In this context, Bayraktar et al. (2013a) show that a dividend barrier strategy is optimal when dividend decisions are made continuously. In practice, h...
Article
The class of spectrally positive Lévy processes is a frequent choice for modelling loss processes in areas such as insurance or operational risk. Dependence between such processes (e.g. between different lines of business) can be modelled with Lévy copulas. This approach is a parsimonious, efficient and flexible method which provides many of the ad...
Article
Stochastic loss reserving with dependence has received increased attention in the last decade. A number of parametric multivariate approaches have been developed to capture dependence between lines of business within an insurer’s portfolio. Motivated by the richness of the Tweedie family of distributions, we propose a multivariate Tweedie approach...
Article
We consider the dual model, which is appropriate for modelling the surplus of companies with deterministic expenses and stochastic gains, such as pharmaceutical, petroleum or commission-based companies. Dividend strategies for this model that can be found in the literature include the barrier strategy (e.g., Avanzi et al., 2007) and the threshold s...
Article
Exploiting embedded supply-chain real options creates powerful opportunities for competitive manufacturing in high-cost environments. Rather than seeking competitiveness through standardization as is common to lean production, real-options reasoning explores opportunities to use supply-chain variability as a strategic weapon. We present an illustra...
Article
We develop a generalization of the World Bank (1994) model of forced saving for retirement. This broader model consists of two tiers of second pillar savings --- mandated and non-mandated (voluntary). Furthermore, the government can set two types of guarantees on the first (mandated) tier --- investment returns and annuity prices --- leading to pos...
Article
We develop a real-options model for optimizing production and sourcing choices under evolutionary supply-chain risk. We model lead time as an endogenous decision and calculate the cost differential required to compensate for the risk exposure coming from lead time. The shape of the resulting cost-differential frontier reveals the term structure of...
Article
The Swiss second pillar of retirement saving features unique properties and remarkable outcomes. These include both high levels of savings and (unforced) annuitization, as well as a non-trivial level of internal cross-subsidies between the two tiers of the system.We formulate a quantitative model of financial flows within this system. We then analy...
Article
In this paper we investigate the potential of Lévy copulas as a tool for modelling dependence between compound Poisson processes and their applications in insurance. We analyse characteristics regarding the dependence in frequency and dependence in severity allowed by various Lévy copula models. Through the introduction of new Lévy copulas and comp...
Article
Full-text available
The Swiss model of retirement savings and benefits distinguishes itself in several aspects. The system is successful in encouraging substantial savings, which are exonerated from tax and guaranteed. The associated market risk is not transferred to the individuals. From an international perspective it is extraordinary that more than half of the Swis...
Article
The dual model with diffusion is appropriate for companies with continuous expenses that are offset by stochastic and irregular gains. Examples include research-based or commission-based companies. In this context, Avanzi and Gerber (2008) showed how to determine the expected present value of dividends, if a barrier strategy is followed. In this pa...
Article
The Swiss model of retirement savings and benefits distinguishes itself in several aspects. The system is successful in encouraging substantial savings, which are exonerated from tax and guaranteed. The associated market risk is not transferred to the individuals. From an international perspective it is extraordinary that more than half of the Swis...
Article
In actuarial risk theory, the introduction of dividend pay-outs in surplus models goes back to Bruno de Finetti (1957). Dividend strategies that can be found in the literature often yield pay-out patterns that are inconsistent with actual practice. One issue is the high variability of the dividend payment rates over time. We aim at addressing that...
Article
Full-text available
In today's world of financial uncertainty, one major public concern is to assess (and possibly improve) the stability of companies that take on risks. Actuaries are aware of that issue for a very long time and have a great experience in modeling the activity of a risk business. During the first part of the twentieth century, they focused on the pro...
Article
Although it is generally agreed that companies are better off with shorter manufacturing lead times, investment in lead time reduction is often difficult to justify using traditional project valuation techniques such as net present value (NPV). In this article, we suggest that evaluating investment in lead time reduction from a real options perspec...
Article
In the dual model, the surplus of a company is a Lévy process with sample paths that are skip-free downwards. In this paper, the aggregate gains process is the sum of a shifted compound Poisson process and an independent Wiener process. By means of Laplace transforms, it is shown how the expectation of the discounted dividends until ruin can be cal...
Article
Organizational practices related to Six Sigma are believed to have resulted in improved organizational outcomes. The academic community, however, continues to lack understanding of the constructs and causal relationships underlying Six Sigma. Hence, discussion of Six Sigma is buffeted by anecdotal experience reported from practice. We evaluate Six...
Article
In his seminal paper, Bruno de Finetti (1957) laid the foundations of what would become an increasingly popular branch of risk theory: the study of dividend strategies. The recent burst of research in this field encouraged the author to carry out a systematic literature review of modern collective risk theory with dividend strategies. This paper ai...
Article
In the dual model, the surplus of a company is a Levy process with sample paths that are skip-free downwards. In this paper, the aggregate gains process is the sum of a shifted compound Poisson process and an independent Wiener process. By means of Laplace transforms, it is shown how the expectation of the discounted dividends until ruin can be cal...
Article
The optimal dividend problem proposed by de Finetti [de Finetti, B., 1957. Su un’impostazione alternativa della teoria collettiva del rischio. In: Transactions of the XVth International Congress of Actuaries, vol. 2. pp. 433–443] is to find the dividend-payment strategy that maximizes the expected discounted value of dividends which are paid to the...