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The purpose of this paper is to consider a discrete‐time, Markov, regime‐switching, affine term‐structure model for valuing bonds and other interest rate securities. The proposed model incorporates the impact of structural changes in (macro)‐economic conditions on interest‐rate dynamics. The market in the proposed model is, in general, incomplete. A modified version of the Esscher transform, namely, a double Esscher transform, is used to specify a price kernel so that both market and economic risks are taken into account.

The market in the proposed model is, in general, incomplete. A modified version of the Esscher transform, namely, a double Esscher transform, is used to specify a price kernel so that both market and economic risks are taken into account.

The authors derive a simple way to give exponential affine forms of bond prices using backward induction. The authors also consider a continuous‐time extension of the model and derive exponential affine forms of bond prices using the concept of stochastic flows.

The methods and results presented in the paper are new.

In the equatorial Pacific, rainfall is affected by global climate phenomena, such as El Niño Southern Oscillation (ENSO). However, current publicly available methodologies for valuing weather derivatives do not account for the influence of ENSO. The purpose of this paper is to develop a complete framework suitable for valuing rainfall derivatives in the equatorial Pacific.

In this paper, we implement a Markov chain for the occurrence of rain and a gamma model for the conditional quantities using vector generalized linear models (VGLM). The ENSO forecast probabilities reported by the International Research Institute for Climate and Society (IRI) are included as independent variables using different alternatives. We then employ the Esscher transform to price rainfall derivatives.

The methodology is applied and calibrated using the historical rainfall data collected at the El Dorado airport weather station in Bogotá. All the estimated coefficients turn out to be significant. The results prove more accurate than those of Markovian gamma models based on purely statistical descriptions of the daily rainfall probabilities.

This procedure introduces the novelty of incorporating variables related to the climatic phenomena, which are the forecast probabilities regularly published for the occurrence of El Niño and La Niña.

This article discusses issues common to the pricing of both insurance and finance. These include increasing collaboration between insurance companies and banks, deregulation of various insurance and finance markets, integrated risk management, and the emergence of financial engineering as a new profession. Rather than attempting to give an exhaustive exposition of the issues at hand, the author highlights developments that, from a methodological point of view, offer new insight into the comparison of pricing mechanisms between insurance and finance.

Many governments are taking measures in support of small and medium-sized enterprises (SMEs) to mitigate the economic impact of the COVID-19 outbreak. This paper presents a theoretical model for evaluating various government measures, including insurance for bank loans, interest rate subsidy, bridge loans and relief of tax burdens.

This paper distinguishes a firm's intrinsic value and book value, where a firm can lose its intrinsic value when it encounters cash-flow crunch. Wang transform is applied to (1) calculating the appropriate level of interest rate subsidy payable to incentivize banks to issue more loans to SMEs and to extend the loan maturity of current debt to the SMEs, (2) describing the frailty distribution for SMEs and (3) defining banks' underwriting capability and overlap index in risk selection.

Government support for SMEs can be in the form of an appropriate level of interest rate subsidy payable to incentivize banks to issue more loans to SMEs and to extend the loan maturity of current debt to the SMEs.

More available data on bank loans would have helped strengthen the empirical studies.

This paper makes policy recommendations of establishing policy-oriented banks or investment funds dedicated to supporting SMEs, developing risk indices for SMEs to facilitate refined risk underwriting, providing SMEs with long-term tax relief and early-stage equity-type investments.

The model highlights the importance of providing bridge loans to SMEs during the COVID-19 disruption to prevent massive business closures.

This paper provides an analytical framework using Wang transform for analyzing the most effective form of government support for SMEs.

The purpose of this paper is to investigate how queueing theory has been applied to derive results for a Sparre Andersen risk process for which the claim inter‐arrival distribution is hyper Erlang.

The paper exploits the duality results between the queueing theory and risk processes to derive explicit expressions for the ultimate ruin probability and moments of time to ruin in this renewal risk model.

This paper derives explicit expressions for the Laplace transforms of the idle/waiting time distribution in GI/HE_r(k_i,λ_i)/1 and its dual HE_r(k_i,λ_i)/G/1. As a consequence, an expression for the ultimate ruin probability is obtained in this model. The relationship between the time of ruin and busy period in M/G/1 queuing system is used to derive the expected time of ruin.

The study of renewal risk process is mostly concentrated on Erlang distributed inter‐claim times. But the Erlang distributions are not dense in the space of all probability distributions and therefore, the paper cannot approximate an arbitrary distribution function by an Erlang one. To overcome this difficulty, the paper uses the hyper Erlang distributions, which can be used to approximate the distribution of any non‐negative random variable.

The purpose of this paper is to provide a scenario‐based risk measure for a portfolio of European‐style derivative securities over a fixed time horizon under the regime switching Black‐Scholes economy.

The risk measure is constructed by using the risk‐neutral probability, the physical probability and a family of subjective probability measures. The subjective probabilities can be interpreted as risk managers or regulators' risk preferences and/or subjective beliefs.

The authors provide closed form expressions for the European option and barrier option.

The results are difficult to apply to a portfolio with many different kinds of options.

The results provide some insights on risk management of portfolios with derivatives.

The paper presents a scenario‐based risk measure for a portfolio of European‐style derivative securities over a fixed time horizon under the regime switching Black‐Scholes economy. Risk management is the most important task for almost all financial industries, although it cannot be claimed that the method and results of this paper solve the problem, it is believed to provide some insights to the problem, albeit theoretical. For vanilla European options and barrier options, the authors obtained a closed form expression for the risk measure. The idea of this paper can be applied to some other exotic options. For portfolios containing different kinds of derivatives, the results of this paper provide some guideline and insights.

The purpose of this paper is to propose a model for ruin‐contingent life annuity (RCLA) contracts under a jump diffusion model, where the dynamics of volatility is governed by the Heston stochastic volatility framework. The paper aims to illustrate that the proposed jump diffusion process, for both asset price and stochastic volatility, will provide a more realistic pricing model for RCLA contracts in comparison to existing models.

Under the assumption of the deterministic withdrawals, the authors use a partial integro differential equation (PIDE) approach to develop the pricing scheme for the fair value of the lump sum charges of RCLA contracts. Consequently, the authors employ an elegant numerical scheme, finite difference method, for solving the PIDEs for the reference portfolio, as well as the volatility. The findings show that a different pricing behaviour of the RCLA contracts under the authors' model parameters is obtained compared to that in the existing literature.

RCLA pricing in the complete market often underestimates the jump risk and the persistent factor in the volatility process. The authors' generalized model shows how these two random sources of risks can be precisely characterized.

The parameter values used in the numerical analysis require more empirical evidence. Hence, in order for more precise pricing practice, the calibration from real data is needed.

The model, as adopted in this study, for pricing of RCLA contracts should provide a general guideline for the commercialization of this product by insurance companies.

The demand for RCLA contracts as an alternative to the commonly‐practised annuitization option has recently increased, rapidly, among the soon‐to‐retire baby boomers. This paper investigates the fair value of this particular product, which could be beneficial to researchers for a better understanding of the product design.

This is the first research paper which prices the RCLA contracts in the incomplete market. The gap between RCLA contract pricing and studies of jump diffusion models for derivative pricing, in the literature, is therefore filled.

Lifetime data are used in many different applied sciences, like biomedicine, engineering, insurance and finance and others. The purpose of this paper is to develop a new acceptance sampling plans for Rama distribution when the mean lifetime test is truncated at a pre-determined time. The minimum sample sizes required to assert the specified life mean is obtained for a given customer’s risk. The operating characteristic function values of the sampling plans and producer’s risk are calculated.

The results are illustrated using numerical examples and a real data set is considered to illustrate the performance of the suggested acceptance sampling plans and how it can be used for the industry applications.

This paper shows a new acceptance sampling plans based on Rama distribution in the particular case when the mean life time test is truncated.

The results calculated in this paper demonstrate the differences between OC values for different distributions taken into account. In particular, OC values of Rama distribution are found to be less than the proposed distribution counterparts.

A variety of equity-linked insurance contracts such as variable annuities (VA) and equity-indexed annuities (EIA) have gained their attractiveness in the past decade because of the bullish equity market and low interest rates. Due to the complexity of their inherent nature, pricing and risk management of these products are quantitatively challenging and therefore have become sources of concern to many insurance companies. From a financial engineer's perspective, the options in VA and those embedded in EIA can be modeled as puts and calls, respectively, and enable the use of numerical option pricing techniques. Additionally, values of VA and EIA move in opposite directions in response to changes in the underlying equity value. Therefore, for insurers who offer both businesses, there are natural offsets or diversification benefits in terms of economic capital (EC) usage. In this chapter, we consider two specific products: the guaranteed minimal account benefit (GMAB) and the point-to-point (PTP) EIA contract, which belong to the VA and EIA classes respectively. Taking into account mortality risk and suboptimal dynamic lapse behavior, we build a framework that quantifies the value of each product and the natural hedging benefits based on risk-neutral option pricing theory. With Monte Carlo simulation and finite difference methods being implemented, an optimum product mixture of those two contracts is achieved that deploys capital the most efficiently.

The purpose of this study is to develop new type of reverse mortgage contract. How to provide adequate services and housing for an increasing number of people that are dependent on the help of others is a crucial question in the European Union (EU). The housing stock in Europe is not fit to support a shift from institutional care to the home-based independent living. Some 90% of houses in the UK and 70%–80% in Germany are not adequately built, as they contain accessibility barriers for people with emerging functional impairments. The available reverse mortgage contracts do not allow for relocation to their own adapted facilities. How to finance the adaptation from housing equity is discussed.

The authors have extended the existing loan reverse mortgage model. Actuarial methods based on the equivalence of the actuarial present values and the multiple decrement approach are used to evaluate premiums for flexible longevity and lifetime long-term care (LTC) insurance for financing adequate facilities.

The adequate, age-friendly housing provision that is appropriate to support the independence and autonomy of seniors with declining functional capacities can lower the cost of health care and improve the well-being of older adults. For financing the development of this kind of facilities for seniors, the authors developed the reverse mortgage scheme with embedded longevity and LTC insurance as a possible financial instrument for better LTC services and housing with care in assisted-living facilities. This kind of facilities should be available for the rapid growth of older cohorts.

The numerical example is based on rather crude numbers, because of lack of data, as the developed reverse mortgage product with LTC insurance is a novelty. Intensity of care and probabilities of care in certain category of care will change after the introduction of this product.

The model results indicate that it is possible to successfully tie an insurance product to the insured and not to the object.

The introduction of this insurance option will allow many older adult with low pension benefits and a substantial home equity to safely opt for a reverse mortgage and benefit from better social care.

While currently available reverse mortgage contracts lapse when the homeowner moves to assisted-living facilities in any EU Member State, in the paper a new method is developed where multiple adjustments of housing to the functional capacities with relocation is possible, under the same insurance and reverse mortgage contract. The case of Slovenia is presented as a numerical example. These insurance products, as a novelty, are portable, so the homeowner can move in own specialised housing unit in assisted-living facilities and keep the existing reverse mortgage contract with no additional costs, which is not possible in the current insurance products. With some small modifications, the method is useful for any EU Member State.