This paper presents analytical representations for an optimal insurance contract under distortion risk measure and in the presence of model uncertainty. We incorporate ambiguity aversion and distortion risk measure through the model of Robert and Therond [(2014) ASTIN Bulletin: The Journal of the IAA, 44(2), 277–302.] as per the framework of Klibanoff et al. [(2005) A smooth model of decision making under ambiguity. Econometrica, 73(6), 1849–1892.]. Explicit optimal insurance indemnity functions are derived when the decision maker (DM) applies Value-at-Risk as risk measure and is ambiguous about the loss distribution. Our results show that: (1) under model uncertainty, ambiguity aversion results in a distorted probability distribution over the set of possible models with a bias in favor of the model which yields a larger risk; (2) a more ambiguity-averse DM would demand more insurance coverage; (3) for a given budget, uncertainties about the loss distribution result in higher risk level for the DM.

We present an asymptotically optimal importance sampling for Monte Carlo simulation of the Laplace transform of exponential Brownian functionals which plays a prominent role in many disciplines. To this end we utilize the theory of large deviations to reduce finding an asymptotically optimal importance sampling measure to solving a calculus of variations problem. Closed-form solutions are obtained. In addition we also present a path to the test of regularity of optimal drift which is an issue in implementing the proposed method. The performance analysis of the method is provided through the Dothan bond pricing model.

It was recently shown that blind source separation (BSS), as originally developed in the signal processing community, can be used in operational modal analysis to separate the responses of a structure into its individual modal contributions. This, in turn, allows the application of simple single-of-degree-freedom techniques to identify the modal parameters of interest. Several publications have recently attempted to give a posteriori physical interpretations to BSS – as initially developed in telecommunication signal processing – when applied to the field of structural dynamics. This paper proposes to follow the route the other way round. It shows that several separation criteria purposely dedicated to operational modal analysis can be deduced from general physical considerations. Three such examples are introduced, based on very different properties that uniquely characterise a structural mode. The first criterion, coined the “principle of shortest envelope”, conjectures that the envelope of a modal response has, among all possible envelopes, the shortest length. That such a principle leads to the governing differential equation of a single-degree-of-freedom oscillator is proved from calculus of variation. The second criterion, coined the “principle of minimum spectral variance”, conjectures that the frequency spectrum of a structural mode is maximally concentrated around its central frequency. Finally, the third criterion, coined the “principle of least spectral complexity”, states that a structural mode has the lowest possible entropy in the frequency domain. All three criteria can be expressed in terms of a mixing matrix whose columns contain the unknown mode shapes. The recovery of the latter is then trivially achieved by minimising the criteria. Extensive simulations show that the proposed criteria lead to figures of merit very similar to those of the state-of-the-art, while at the same time providing physical insight that other algorithms issued form the signal processing community may dramatically lack.

The stationary characteristics of an n-component periodic review system which is subject to stochastic deterioration (but not to failure) are investigated. When the n-component vector which expresses the state of deterioration of the system pierces a certain surface the entire multicomponent system is replaced by items of identical cost structure at the time of the next review. In the absence of this situation nothing is replaced. It is assumed that there is a fixed cost associated with each replacement and that the operating cost of each item is a strictly increasing function of its state of deterioration. The conditions for minimizing the long-term cost of maintaining a system which operates under the stated policy were found through solution of a problem in variational calculus. Two examples are worked. A useful graph which aids in the solution of such problems is provided.