We use methods of algebraic geometry to find new, effective methods for detecting the identifiability of symmetric tensors. In particular, for ternary symmetric tensors T of degree 7, we use the analysis of the Hilbert function of a finite projective set, and the Cayley-Bacharach property, to prove that, when the Kruskal's ranks of a decomposition of T are maximal (a condition which holds outside a Zariski closed set of measure 0), then the tensor T is identifiable, i.e. the decomposition is unique, even if the rank lies beyond the range of application of both the Kruskal's and the reshaped Kruskal's criteria.
We introduce a new criterion which tests if a given decomposition of a given ternary form T of even degree is unique. The criterion is based on the analysis of the Hilbert function of the projective set of points Z associated to the decomposition, and on the Terracini's Lemma which describes tangent spaces to secant varieties. The criterion works in a range for the length of the decomposition which is equivalent to the range in which the reshaped Kruskal's criterion (see [1]) works. Our criterion determines an algorithm for the identifiability of T which is sensibly faster than algorithms based on the reshaped Kruskal's criterion, especially when the set of points Z is not in general position.
We consider a constructive model for asset price bubbles, where the market price W is endogenously determined by the trading activity on the market and the fundamental price W F is exogenously given, as in [28]. To justify W F from a fundamental point of view, we embed this constructive approach in the martingale theory of bubbles, see [26] and [10], by showing the existence of a flow of equivalent martingale measures for W , under which W F equals the expectation of the discounted future cash flow.As an application, we study bubble formation and evolution in a financial network.
This paper assesses the risk of a mass lapse event in life insurance. The rarity of the event and the complexity of policyholder behavior make the risk assessment of such a scenario difficult. Using a simulation study, we evaluate how different estimation methods can assess the risk of this scenario, using panel data at the company level. We then use the best-performing method to estimate the probability distribution function of a mass cancellation event in the United States and Germany. We identify dependencies of the event on company and country characteristics, which have not been taken into account by regulating agencies. We also find that the current mass lapse scenario in Solvency II has no empirical foundation for the German market. We show that an empirically valid scenario leads to a significantly lower solvency capital requirement for the average German life insurer.
This paper assesses the risk of a mass lapse event in life insurance. The rarity of the event and the complexity of policyholder behavior make the risk assessment of such a scenario difficult. Using a simulation study, we evaluate how different estimation methods can assess the risk of this scenario, using panel data at the company level. We then use the best-performing method to estimate the probability distribution function of a mass cancellation event in the United States and Germany. We identify dependencies of the event on company and country characteristics, which have not been taken into account by regulating agencies. We also find that the current mass lapse scenario in Solvency II has no empirical foundation for the German market. We show that an empirically valid scenario leads to a significantly lower solvency capital requirement for the average German life insurer.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.