Risk and Decision Analysis

Engineering risk analysis, traditionally applied to engineering systems, relies on the decomposition of the system under study into subsystems and of the scenarios affecting it into basic events. The same principles are applied to the study of insolvency. In particular, we introduce a model designed to estimate insolvency risk for property and casualty insurance firms. Specifically, our approach relies on a set of models, which together describe how an insurance firm operates. Beyond firm-specific estimation of insolvency risk, our objective is to gain insights into the drivers behind insolvency and to compare those with industry wisdom and historical data. One of our findings suggests that the current practice of adapting pricing to market conditions (soft or hard markets) may in fact be sensible in terms of insolvency risk. Another finding shows that while small companies are associated with higher insolvency risk, the effect of size is noticeable either for very small firms or for firms who do not adjust their sales level to their surplus value.

This paper discusses facets of the insurance–finance convergence and their competition. Differences and similarities are emphasized and examples are used to highlight their approaches to pricing. We emphasize situations that are particular to the insurance world, such as non normal risks, catastrophic risks, contagions, and other situations where risks are not easily defined. Some questions relating to the efficiency of portfolio securitization are also raised in light of the latent and macroeconomic risks that have pervaded insurance and financial insurance portfolios during the financial crisis.

Recent results in optimal stopping theory have shown that a ‘bang-bang’ (buy or sell immediately) style of trading strategy is in some sense optimal provided the asset's price dynamics follow certain familiar stochastic processes. This paper constructs a reward-to-variability ratio (the mixed Sharpe ratio) that is sufficient for this strategy's implementation. The use of this ratio for optimal portfolio selection is discussed and evidence for it varying over time is found. The performances of the ‘bang-bang’ and ‘buy-and-hold’ trading strategies are compared and the former is found to be significantly more profitable.

Comonotonicity has proved to be a powerful and useful tool in financial economics and actuarial science. Jouini and Napp [Decision in Economics and Finance 27(2) (2004), 153–166] generalized it to a new concept called conditional comonotonicity. While preserving the advantage of being analytically tractable, the extra freedom of the choice of the conditioning map or sigma-field makes this new concept more flexible than the classical concept of comonotonicity. This article serves to provide a systemic overview, together with some of its applications, of this relatively new notion.

We study a model of an insurance company whose surplus is represented by a pure diffusion. The company is allowed to buy proportional reinsurance and invest its surplus in a Black–Sholes financial market. Further, it is assumed that transaction cost rate of the reinsurance decreases linearly while the insurance company buys more reinsurance. We consider two optimization criteria – minimizing probability of ruin and maximizing expected exponential utility of terminal wealth for a fixed time. Corresponding Hamilton–Jacobi–Bellman (HJB) equations are analyzed; consequently we find explicit expressions of the minimal ruin probability, maximal expected terminal utility, and their associated optimal reinsurance–investment strategies via various parameter conditions. We observe from the explicit results that for some special parameter cases, the optimal investment–reinsurance strategies coincide under the two optimization criteria; i.e., Ferguson's longstanding conjecture on the relation between the two problems holds.

In this paper, we apply the elasticity approach to optimal asset allocation problems in discrete-time setting. In particular, firstly, for a portfolio optimization problem, which targets to maximize the expected utility of the terminal wealth of a portfolio of an option, the underlying stock, and the risk-free bond, the elasticity approach can decompose this problem into a reduced optimization problem, consisting of only the stock and bond, and a pure delta neutral hedging problem. This decomposition provides a discrete-time version of the optimal alternative to the delta hedge, which was initially proposed in continuous time. Moreover, the general principle given by the pure delta neutral strategy is analyzed in our setting. Secondly, the same approach is applied to an optimal investment problem with defaultable securities, and show that this problem is essentially the same as the above mentioned reduced optimization problem. This work can be regarded as an extension of the elasticity approach in Kraft [Mathematical Methods of Operations Research 58(1) (2003), 159–182] to discrete-time models, and it shows that this approach can largely deduce the asset allocation problems in complete market.