Reinsurers may default when they have to pay large claims to insurers but are unable to fulfill their obligations due to various reasons such as catastrophic events, underwriting losses, inadequate capitalization, or financial mismanagement. This paper studies the problem of optimal reinsurance design from the perspectives of both the insurer and reinsurer when the insurer faces the potential default risk of the reinsurer. If the insurer aims to minimize the convex distortion risk measure of his retained loss, we prove the optimality of a stop-loss treaty when the promised ceded loss function is charged by the expected value premium principle and the reinsurer offers partial recovery in the event of default. For any fixed premium loading set by the reinsurer, we then derive the explicit expressions of optimal deductible levels for three special distortion functions, including the TVaR, Gini, and PH transform distortion functions. Under these three explicit distortion risk measures adopted by the insurer, we seek the optimal safety loading for the reinsurer by maximizing her net profit where the reserve capital is determined by the TVaR measure and the cost is governed by the expectation. This procedure ultimately leads to the Bowley solution between the insurer and the reinsurer. We provide several numerical examples to illustrate the theoretical findings. Sensitivity analyses demonstrate how different settings of default probability, recovery rate, and safety loading affect the optimal deductible values. Simulation studies are also implemented to analyze the effects induced by the default probability and recovery rate on the Bowley solution.

This paper studies a Pareto-optimal reinsurance problem when the contract is subject to default of the reinsurer. We assume that the reinsurer can invest a share of its wealth in a risky asset and default occurs when the reinsurer's end-of-period wealth is insufficient to cover the indemnity. We show that without the solvency regulation, the optimal indemnity function is of excess-of-loss form, regardless of the investment decision. Under the solvency regulation constraint, by assuming the investment decision remains unchanged, the optimal indemnity function is characterized element-wisely. Partial results are derived when both the indemnity function and investment decision are impacted by the solvency regulation. Numerical examples are provided to illustrate the implications of our results and the sensitivity of solution to the model parameters.

In this paper, we study the pricing of vulnerable Asian options with liquidity risk. We employ general Lévy processes to capture the changes in the liquidity discount factors and the information processes of all assets. In the proposed pricing model, we obtain the closed-form pricing formula of vulnerable Asian options using the Fourier transform methods. Finally, the derived pricing formula is used to illustrate the effects of asymmetric jump risk, and the effects are relatively stable on (vulnerable) Asian options with different moneynesses.

This paper introduces an integrated asset-liability management model that allows for the joint quantitative analysis of capital structure choices, pension fund allocation decisions and rational pricing of liabilities. We confirm that capital structure decisions have a substantial impact on the value of pension claims, and we provide a quantitative assessment of the mispricing induced by the use of an arbitrary regulatory discount rate. We also present a quantitative assessment of the asset substitution effect implied by a change in the pension fund allocation to risky assets taking place after the corporate and pension obligation claims have been issued.

In this paper, a discrete-time framework is proposed to value power exchange options with counterparty default risk, where counterparty risk is considered in a reduced-form setting and the variance processes of the underlying assets are captured by GARCH processes. In addition, the proposed model allows for the correlation between the intensity of default and the variances of the underlying assets by breaking down the total risk into systematic and idiosyncratic components. By dint of measure-change techniques and characteristic functions, we obtain the closed-form pricing formula for the value of power exchange options with counterparty default risk. Finally, numerical results are presented to show the power exchange option values.

Many fiscal federal scholars argue, often implicitly, that transfer dependence generally bolsters subnational creditworthiness by signalling a higher likelihood of national bailouts for distressed governments. This article argues that dependence fails to bestow general benefits on local borrowers because it suggests an inability to generate additional revenues in the event of fiscal distress, and because this inability does not, contrary to the expectations of many, necessarily translate into higher bailout expectations. Ultimately it is the nature, not the level, of transfers that affects local creditworthiness, whether through bailout or non-bailout channels. Stable and predictable payments, including robust equalization systems, support local creditworthiness, while volatile and unpredictable transfers do not. The article supports these arguments with a review of documents issued by the major international credit rating agencies and cross-national statistical analyses of bailout probabilities and standalone credit ratings issued by Moody’s Investors Service. It also discusses the implications of the findings for work on the fiscal discipline of subnational governments.

In a typical equity-linked life insurance contract, the insurance company is entitled to a share of return surpluses as compensation for the return guarantee granted to the policyholders. The set of possible contract terms might, however, be restricted by a regulatory default constraint — a fact that can force the two parties to initiate sub-optimal insurance contracts. We show that this effect can be mitigated if regulatory policy is more flexible. We suggest that the regulator implement a traffic light system where companies are forced to reduce the riskiness of their asset allocation in distress. In a utility-based framework, we show that the introduction of such a system can increase the benefits of the policyholder without deteriorating the benefits of the insurance company. At the same time, default probabilities (and thus solvency capital requirements) can be reduced.

The Management Board of the UK Actuarial Profession is undertaking a thought leadership cross-practice research project on the use of discount rates by UK actuaries. The timing for this research is particularly appropriate as there is a convergence of interest in discount rates from within and outside of the Profession. Discount rates are at the heart of most actuarial calculations and are of significant public interest. As part of this project the Management Board wants a full and open debate on the significant issues and this paper is the next step in stimulating that debate, giving another opportunity to influence the future direction of the project.

The Management Board set up a small cross-practice steering committee to drive the project. The Discount Rate Steering Committee identified five areas of work that would be needed to achieve the project's overall objectives:

1. (1) A survey of current practices.

2. (2) A survey of existing research and debate.

3. (3) Developing a common language for communicating discount rates and risk.

4. (4) Developing a common framework for the future where appropriate.

5. (5) Considering the impact of any changes.

Although the Profession does not set standards for technical work it still has a significant role for undertaking research in the public interest which supports the competence of its members and the furtherance of actuarial science.

Chinu Patel and Chris Daykin were commissioned to undertake the first part of this work and they presented their preliminary output at a forum of thought leaders across the Profession and externally on 23 March 2010. Their report “Actuaries and Discount Rates” was subsequently published in May 2010 and presented the results of their initial research into past and current practice in the setting of discount rates in the UK, and a survey of existing research and debate. A summary of that report is included in Section 2 of this paper.

Following consultation both within and outside the Actuarial Profession, this interim paper now takes forward the ideas and initial steps developed by Patel & Daykin and looks at developing a common language and framework for using discount rates in actuarial work. The Discount Rate Steering Committee is making a number of recommendations to the Profession which are intended to help actuaries speak clearly and with authority in future debates about discount rates and to support actuaries in communicating impartially and effectively. The recommendations are set out in Section 6 of the report following the development of the framework in Sections 3–5. As part of further developing the recommendations to the Profession, the Discount Rate Steering Committee is seeking views from stakeholders from inside and outside of the Profession. This will be undertaken throughout January and February 2011 and, as part of this process, the report will be presented at sessional research events in Edinburgh (17 January 2011) and London (31 January 2011). The Discount Rate Steering Committee is committed to seeking feedback on the recommendations and hopes this paper will give those inside and outside the Profession an opportunity to add to the dialogue so that as wide a range of potential views as possible is heard.

In this paper, the steering committee has concentrated on the more technical aspects of developing a framework for communicating discount rates and associated risks and the report is aimed primarily at actuaries. But the committee is mindful of the need to help actuaries communicate more clearly with those outside the Profession. During the first half of 2011, the steering committee will therefore concentrate on producing a document in less technical language to help non-actuaries understand the issues around the selection and use of discount rates and to help actuaries in their communication with stakeholders.

The paper examines a type of insurance contract for which secondary markets do exist: default risk insurance is implicit in corporate bonds and other risky debts. It applies risk neutral martingale measure pricing to evaluate the option for a borrower with default risk, to prepay a fixed rate loan. A simple “matchbox” example is presented with a spreadsheet treatment.