On the Optimal Dividend Problem for Insurance Risk Models with Surplus-Dependent Premiums

This paper concerns an optimal dividend distribution problem for an insurance company with surplus-dependent premium. In the absence of dividend payments, such a risk process is a particular case of so-called piecewise deterministic Markov processes. The control mechanism chooses the size of dividend payments. The objective consists in maximazing the sum of the expected cumulative discounted dividend payments received until the time of ruin and a penalty payment at the time of ruin, which is an increasing function of the size of the shortfall at ruin. A complete solution is presented to the corresponding stochastic control problem. We identify the associated Hamilton-Jacobi-Bellman equation and find necessary and sufficient conditions for optimality of a single dividend-band strategy, in terms of particular Gerber-Shiu functions. A number of concrete examples are analyzed

On the Bail-Out Optimal Dividend Problem

This paper studies the optimal dividend problem with capital injection under the constraint that the cumulative dividend strategy is absolutely continuous. We consider an open problem of the general spectrally negative case and derive the optimal solution explicitly using the fluctuation identities of the refracted-reflected L\'evy process. The optimal strategy as well as the value function are concisely written in terms of the scale function. Numerical results are also provided to confirm the analytical conclusions.Comment: To appear in Journal of Optimization Theory and Applications. Keywords: stochastic control, scale functions, refracted-reflected L\'evy processes, bail-out dividend proble

On Fair Reinsurance Premiums; Capital Injections in a Perturbed Risk Model

We consider a risk model where deficits after ruin are covered by a new type of reinsurance contract that provides capital injections. To allow the insurance company's survival after ruin, the reinsurer injects capital only at ruin times caused by jumps larger than a chosen retention level. Otherwise capital must be raised from the shareholders for small deficits. The problem here is to determine adequate reinsurance premiums. It seems fair to base the net reinsurance premium on the discounted expected value of any future capital injections. Inspired by the results of Huzak et al. (2004) and Ben Salah (2014) on successive ruin events, we show that an explicit formula for these reinsurance premiums exists in a setting where aggregate claims are modeled by a subordinator and a Brownian perturbation. Here ruin events are due either to Brownian oscillations or jumps and reinsurance capital injections only apply in the latter case. The results are illustrated explicitly for two specific risk models and in some numerical examples.Comment: 23 pages, 3 figure

Derivatives and Corporate Risk Management: Participation and Volume Decisions in the Insurance Industry

The use of derivatives in corporate risk management has grown rapidly in recent years. In this paper, the authors explore the factors that influence the use of financial derivatives in the U.S. insurance industry. Their objective is to investigate the motivations for corporate risk management The authors use regulatory data on individual holdings and transactions in derivative markets. According to modern finance theory, shares of widely held corporations are held by diversified investors who operate in frictionless and complete markets and eliminate non-systematic risk through their portfolio choices. But this theory has been challenged by new hypotheses that take into account market imperfections, information asymmetries and incentive conflicts as motivations for corporate managers to change the risk/return profile of their firm. The authors develop a set of hypotheses regarding the hedging behavior of insurers and perform tests on a sample of life and property-liability insurers to test them. The sample consists of all U.S. life and property-liability insurers reporting to the NAIC. The authors investigate the decision to conduct derivatives transactions and the volume of transactions undertaken. There are two primary theories about the motivations for corporate risk management - maximization of shareholder value and maximization of managerial utility. The authors discuss these theories, the hypotheses they develop from them , and specify variables to test their hypotheses. They posit the following rationales for why corporations may choose to engage in risk management and also specify variables that help them study the use of these rationales by insurance firms: to avoid the costs of financial distress; to hedge part of their investment default/volatility/liquidity risks; to avoid shocks to equity that result in high leverage ratios; to minimize taxes and enhance firm value by reducing the volatility of earnings; to maximize managerial utility. The authors argue that the use of derivatives for speculative purposes in the insurance industry is not common. The authors analyze the decision by insurers to enter the market and their volume of transactions. They use probit analysis to study the participation decision and Tobit analysis along with Cragg's generalization of the Tobit analysis to study volume. The results provide support for the authors' hypothesis that insurers hedge to maximize shareholder value. The analysis provides only weak support for the managerial utility hypothesis. Insurers are motivated to use financial derivatives to reduce the expected costs of financial distress. There is also evidence that insurers use derivatives to hedge asset volatility and exchange rate risks. There is also evidence that there are significant economies of scale in running derivatives operations - only large firms and/or those with higher than average risk exposure find it worthwhile to pay the fixed cost of setting up a derivatives operation. Overall, insurers with higher than average asset risk exposures use derivative securities.

Dynamic Models of the Insurance Markets

This is a multi-essay dissertation in the area of dynamic models of the insurance markets. I study issues in insurance markets by examining individual behavior and industry performance in dynamic settings. My first essay studies household life insurance demand and saving decisions by applying a heterogeneous-agent life cycle model with wage shocks and mortality shocks. This essay proposes the most important determinants of household life insurance demand, and shows the joint decision of life insurance purchase between couples. My second essay focuses on the property-liability insurance market, and aims to study the impact of one catastrophe event on an insurer’s underwritings and capital raising strategy. The two-period cash flow model is built to also explore what kind of insurers can benefit from catastrophic risk underwritings. My third essay extends the second essay by incorporating a dynamic cash flow model with a series of loss shocks. I find the dynamic interaction between the insurer’s balance sheet and its capital rationing resulting from loss shocks. The model generates a non-cyclical behavior of output changes in the insurance market, and this suggests the current asymmetric, unpredictable and random underwriting cycles are temporary responses to loss shocks