Risks, Volume 6, Issue 1 (March 2018) – 23 articles

An arbitrage portfolio provides a cash flow that can never be negative at zero cost. We define the weaker concept of a “desirable portfolio” delivering cash flows with negative risk at zero cost. Although these are not completely risk-free investments and subject to the risk measure used, they can provide attractive investment opportunities for investors. We investigate in detail the theoretical aspects of this portfolio selection procedure and the existence of such opportunities in fixed income markets. Then, we present two applications of the theory: one in analyzing market integration problem and the other in gauging the credit quality of defaultable bonds in a portfolio. We also discuss the model calibration and provide some numerical illustrations. Full article

We are interested in obtaining forecasts for multiple time series, by taking into account the potential nonlinear relationships between their observations. For this purpose, we use a specific type of regression model on an augmented dataset of lagged time series. Our model is inspired by dynamic regression models (^{Pankratz 2012}), with the response variable’s lags included as predictors, and is known as Random Vector Functional Link (RVFL) neural networks. The RVFL neural networks have been successfully applied in the past, to solving regression and classification problems. The novelty of our approach is to apply an RVFL model to multivariate time series, under two separate regularization constraints on the regression parameters. Full article

Since its origins and numerous applications in material science, the Birnbaum–Saunders family of distributions has now found widespread uses in some areas of the applied sciences such as agriculture, environment and medicine, as well as in quality control, among others. It is able to model varied data behaviour and hence provides a flexible alternative to the most usual distributions. The family includes Birnbaum–Saunders and log-Birnbaum–Saunders distributions in univariate and multivariate versions. There are now well-developed methods for estimation and diagnostics that allow in-depth analyses. This paper gives a detailed review of existing methods and of relevant literature, introducing properties and theoretical results in a systematic way. To emphasise the range of suitable applications, full analyses are included of examples based on regression and diagnostics in material science, spatial data modelling in agricultural engineering and control charts for environmental monitoring. However, potential future uses in new areas such as business, economics, finance and insurance are also discussed. This work is presented to provide a full tool-kit of novel statistical models and methods to encourage other researchers to implement them in these new areas. It is expected that the methods will have the same positive impact in the new areas as they have had elsewhere. Full article

In this work, the non-homogeneous risk model is considered. In such a model, claims and inter-arrival times are independent but possibly non-identically distributed. The easily verifiable conditions are found such that the ultimate ruin probability of the model satisfies the exponential estimate $exp\{-\varrho u\}$ for all values of the initial surplus $u⩾0$ . Algorithms to estimate the positive constant $\varrho$ are also presented. In fact, these algorithms are the main contribution of this work. Sharpness of the derived inequalities is illustrated by several numerical examples. Full article

In this paper, we offer a novel class of utility functions applied to optimal portfolio selection. This class incorporates as special cases important measures such as the mean-variance, Sharpe ratio, mean-standard deviation and others. We provide an explicit solution to the problem of optimal portfolio selection based on this class. Furthermore, we show that each measure in this class generally reduces to the efficient frontier that coincides or belongs to the classical mean-variance efficient frontier. In addition, a condition is provided for the existence of the a one-to-one correspondence between the parameter of this class of utility functions and the trade-off parameter $\lambda$ in the mean-variance utility function. This correspondence essentially provides insight into the choice of this parameter. We illustrate our results by taking a portfolio of stocks from National Association of Securities Dealers Automated Quotation (NASDAQ). Full article

The general problem of asset pricing when the discount rate differs from the rate at which an asset’s cash flows accrue is considered. A pricing kernel framework is used to model an economy that is segmented into distinct markets, each identified by a yield curve having its own market, credit and liquidity risk characteristics. The proposed framework precludes arbitrage within each market, while the definition of a curve-conversion factor process links all markets in a consistent arbitrage-free manner. A pricing formula is then derived, referred to as the across-curve pricing formula, which enables consistent valuation and hedging of financial instruments across curves (and markets). As a natural application, a consistent multi-curve framework is formulated for emerging and developed inter-bank swap markets, which highlights an important dual feature of the curve-conversion factor process. Given this multi-curve framework, existing multi-curve approaches based on HJM and rational pricing kernel models are recovered, reviewed and generalised and single-curve models extended. In another application, inflation-linked, currency-based and fixed-income hybrid securities are shown to be consistently valued using the across-curve valuation method. Full article

This paper presents the first methodological proposal of estimation of the $\mathsf{\Lambda }VaR$ . Our approach is dynamic and calibrated to market extreme scenarios, incorporating the need of regulators and financial institutions in more sensitive risk measures. We also propose a simple backtesting methodology by extending the $VaR$ hypothesis-testing framework. Hence, we test our $\mathsf{\Lambda }VaR$ proposals under extreme downward scenarios of the financial crisis and different assumptions on the profit and loss distribution. The findings show that our $\mathsf{\Lambda }VaR$ estimations are able to capture the tail risk and react to market fluctuations significantly faster than the $VaR$ and expected shortfall. The backtesting exercise displays a higher level of accuracy for our $\mathsf{\Lambda }VaR$ estimations. Full article

Audit mechanisms frequently take place in the context of repeated relationships between auditor and auditee. This paper focuses attention on the insurance fraud problem in a setting where insurers repeatedly verify claims satisfied by service providers (e.g., affiliated car repairers or members of managed care networks). We highlight a learning bias that leads insurers to over-audit service providers at the beginning of their relationship. The paper builds a bridge between the literature on optimal audit in insurance and the exploitation/exploration trade-off in multi-armed bandit problems. Full article

This paper presents a novel risk-based approach for an optimal asset allocation problem with default risk, where a money market account, an ordinary share and a defaultable security are investment opportunities in a general non-Markovian economy incorporating random market parameters. The objective of an investor is to select an optimal mix of these securities such that a risk metric of an investment portfolio is minimized. By adopting a sub-additive convex risk measure, which takes into account interest rate risk, as a measure for risk, the investment problem is discussed mathematically in a form of a two-player, zero-sum, stochastic differential game between the investor and the market. A backward stochastic differential equation approach is used to provide a flexible and theoretically sound way to solve the game problem. Closed-form expressions for the optimal strategies of the investor and the market are obtained when the penalty function is a quadratic function and when the risk measure is a sub-additive coherent risk measure. An important case of the general non-Markovian model, namely the self-exciting threshold diffusion model with time delay, is considered. Numerical examples based on simulations for the self-exciting threshold diffusion model with and without time delay are provided to illustrate how the proposed model can be applied in this important case. The proposed model can be implemented using Excel spreadsheets. Full article

The relevance of critical illness coverage and life insurance in cause-specific mortality conditions is increasing in many industrialized countries. Specific conditions on the illness and on death event, providing cheapest premiums for the insureds and lower obligations for the insurers, constitute interesting products in an insurance market looking to offer appealing products. On the other hand, the systematic improvement in longevity gives rise to a market with agents getting increasingly older, and the insurer pays attention to this trend. There are financial contracts joined with insurance coverage, and this particularly happens in the case of the so-called insured loan. Insured loans are financial contracts often proposed together with a term life insurance in order to cover the lender and the heirs against the borrower’s death event within the loan duration. This paper explores new insurance products that, linked to an insured loan, are founded on specific illness hypotheses and/or cause-specific mortality. The aim is to value how much the insurance costs lighten with respect to the traditional term insurance. The authors project cause-specific mortality rates and specific diagnosis rates, in this last case overcoming the discontinuities in the data. The new contractual schemes are priced. Numerical applications also show, with several graphs, the rates projection procedure and plenty of tables report the premiums in the new proposed contractual forms. The complete amortization schedule closes the work. Full article

Little in the scholarly economics literature is directed specifically to the performance of stable value funds, although they occupy a leading place among retirement investment vehicles. They are currently offered in more than one-third of all defined contribution plans in the USA, with more than $800 billion of assets under management. This paper rigorously examines their performance throughout the entire period since their inception in 1973. We produce a composite index of stable value returns. We next conduct mean-variance analysis, Sharpe and Sortino ratio analysis, stochastic dominance analysis, and optimal multi-period portfolio composition analysis. Our evidence suggests that stable value funds dominate (on average) two major asset classes based on a historical analysis, and that they often occupy a significant position in optimized portfolios across a broad range of risk aversion levels. We discuss factors that contributed to stable value funds’ past performance and whether they can continue to perform well into the future. We also discuss considerations regarding whether or not to include stable value as an element in target date funds within defined contribution pension plans. Full article

Composite models have received much attention in the recent actuarial literature to describe heavy-tailed insurance loss data. One of the models that presents a good performance to describe this kind of data is the composite Weibull–Pareto (CWL) distribution. On this note, this distribution is revisited to carry out estimation of parameters via mle and mle2 optimization functions in R. The results are compared with those obtained in a previous paper by using the nlm function, in terms of analytical and graphical methods of model selection. In addition, the consistency of the parameter estimation is examined via a simulation study. Full article

The design and development of post-retirement income products require the assessment of longevity risk, as well as a basis for hedging these risks. Most indices for longevity risk are age-period based. We develop and assess a cohort-based value index for life insurers and pension funds to manage longevity risk. There are two innovations in the development of this index. Firstly, the underlying variables of most existing longevity indices are based on mortality experience only. The value index is based on the present value of future cash flow obligations, capturing all the risks in retirement income products. We use the index to manage both longevity risk and interest rate risk. Secondly, we capture historical dependencies between ages and cohorts with a cohort-based stochastic mortality model. We achieve this by introducing age-dependent model parameters. With our mortality model, we obtain realistic cohort correlation structures and improve the fitting performance, particularly for very old ages. Full article

Prospective customers of financial and insurance products can be targeted based on the profit the provider expects to earn from them. We present a model for individual expected profit and two alternatives for calculating optimal personalized prices that maximize the expected profit. For one of these alternatives, we obtain a closed-form expression for the price offered to each prospective customer; for the other, we need to use a numerical approximation. In both approaches, the profits generated by prospective customers are not immediately observed, given that the products sold by these companies have a risk component. We assume that willingness to pay is heterogeneous and apply our methodology using real data from a European insurance company. Our study indicates that a substantial boost in profits can be expected when applying the simplest optimal pricing method proposed. Full article

The ability and willingness of health care workers to report for work during a pandemic are essential to pandemic response. The main contribution of this article is to examine the relationship between risk perception of personal and work activities and willingness to report for work during an influenza pandemic. Data were collected through a quantitative Web-based survey sent to health care workers on the island of Montreal. Respondents were asked about their perception of various risks to obtain index measures of risk perception. A multinomial logit model was applied for the probability estimations, and a factor analysis was conducted to compute risk perception indexes (scores). Risk perception associated with personal and work activities is a significant predictor of intended presence at work during an influenza pandemic. This means that correcting perceptual biases should be a public policy concern. These results have not been previously reported in the literature. Many organizational variables are also significant. Full article

We introduce a multistep-ahead forecasting methodology that combines empirical mode decomposition (EMD) and support vector regression (SVR). This methodology is based on the idea that the forecasting task is simplified by using as input for SVR the time series decomposed with EMD. The outcomes of this methodology are compared with benchmark models commonly used in the literature. The results demonstrate that the combination of EMD and SVR can outperform benchmark models significantly, predicting the Standard & Poor’s 500 Index from 30 s to 25 min ahead. The high-frequency components better forecast short-term horizons, whereas the low-frequency components better forecast long-term horizons. Full article

This paper extends the work of Yuen et al. (2013), who obtained explicit results for the discount-free Gerber–Shiu function for a compound binomial risk model in the presence of delayed claims and a randomized dividend strategy with a zero threshold level. Specifically, we establish a recursion method for computing the Gerber–Shiu expected discounted penalty function, which entails a number of important quantities in ruin theory, within the framework of the compound binomial aggregate claims with delayed by-claims and randomized dividends payable at a non-negative threshold level. Full article

This paper studies the valuation of real options when the cost of investment jumps at a random time. Three valuation formulas are derived. The first expresses the value of the project in terms of a collection of knockout barrier claims. The second identifies the premium relative to a project with delayed investment right and prices its components. The last one identifies the premium/discount relative to a project with constant cost equal to the post-jump cost and prices its components. All formulas are in closed form. The behavior of optimal investment boundaries and valuation components are examined. Full article

In the nearly thirty years since Hans Buhlmann (Buhlmann (1987)) set out the notion of the Actuary of the Third Kind, the connection between Actuarial Science (AS) and Mathematical Finance (MF) has been continually reinforced. As siblings in the family of Risk Management techniques, practitioners in both fields have learned a great deal from each other. The collection of articles in this volume are contributed by scholars who are not only experts in areas of AS and MF, but also those who present diverse perspectives from both industry and academia. Topics from multiple areas, such as Stochastic Modeling, Credit Risk, Monte Carlo Simulation, and Pension Valuation, among others, that were maybe thought to be the domain of one type of risk manager are shown time and again to have deep value to other areas of risk management as well. The articles in this collection, in my opinion, contribute techniques, ideas, and overviews of tools that specialists in both AS and MF will find useful and interesting to implement in their work. It is also my hope that this collection will inspire future collaboration between those who seek an interdisciplinary approach to risk management. Full article

We propose a Traffic Light approach to backtesting Expected Shortfall which is completely consistent with, and analogous to, the Traffic Light approach to backtesting VaR (Value at Risk) initially proposed by the Basel Committee on Banking Supervision in their 1996 consultative document Basle Committee on Banking Supervision (1996). The approach relies on the generalized coverage test for Expected Shortfall developed in Costanzino and Curran (2015). Full article

Optimal dividend payment under a ruin constraint is a two objective control problem which—in simple models—can be solved numerically by three essentially different methods. One is based on a modified Bellman equation and the policy improvement method (see Hipp (2003)). In this paper we use explicit formulas for running allowed ruin probabilities which avoid a complete search and speed up and simplify the computation. The second is also a policy improvement method, but without the use of a dynamic equation (see Hipp (2016)). It is based on closed formulas for first entry probabilities and discount factors for the time until first entry. Third a new, faster and more intuitive method which uses appropriately chosen barrier levels and a closed formula for the corresponding dividend value. Using the running allowed ruin probabilities, a simple test for admissibility—concerning the ruin constraint—is given. All these methods work for the discrete De Finetti model and are applied in a numerical example. The non stationary Lagrange multiplier method suggested in Hipp (2016), Section 2.2.2, also yields optimal dividend strategies which differ from those in all other methods, and Lagrange gaps are present here. Full article