Identifiability for a class of symmetric tensors

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 rank 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

Financial asset bubbles in banking networks

We consider a banking network represented by a system of stochastic differential equations coupled by their drift. We assume a core-periphery structure, and that the banks in the core hold a bubbly asset. The banks in the periphery have not direct access to the bubble, but can take initially advantage from its increase by investing on the banks in the core. Investments are modeled by the weight of the links, which is a function of the robustness of the banks. In this way, a preferential attachment mechanism towards the core takes place during the growth of the bubble. We then investigate how the bubble distort the shape of the network, both for finite and infinitely large systems, assuming a non vanishing impact of the core on the periphery. Due to the influence of the bubble, the banks are no longer independent, and the law of large numbers cannot be directly applied at the limit. This results in a term in the drift of the diffusions which does not average out, and that increases systemic risk at the moment of the burst. We test this feature of the model by numerical simulations.Comment: 33 pages, 6 table

The Forward Smile in Local–Stochastic Volatility Models

We introduce an asymptotic expansion for forward start options in a multi-factor local-stochastic volatility model. We derive explicit approximation formulas for the so-called forward implied volatility which can be useful to price complex path-dependent options, as cliquets. The expansion involves only polynomials and can be computed without the need for numerical procedures or special functions. Recent results on the exploding behaviour of the forward smile in the Heston model are confirmed and generalized to a wider class of local-stochastic volatility models. We illustrate the effectiveness of the technique through some numerical tests. Mathematica codes are freely available on the authors' website

The Forward Smile in Local–Stochastic Volatility Models

We introduce an asymptotic expansion for forward start options in a multi-factor local-stochastic volatility model. We derive explicit approximation formulas for the so-called forward implied volatility which can be useful to price complex path-dependent options, as cliquets. The expansion involves only polynomials and can be computed without the need for numerical procedures or special functions. Recent results on the exploding behaviour of the forward smile in the Heston model are confirmed and generalized to a wider class of local-stochastic volatility models. We illustrate the effectiveness of the technique through some numerical tests. Mathematica codes are freely available on the authors' website

Generalized Feynman-Kac Formula under volatility uncertainty

In this paper we provide a generalization of a Feynmac-Ka\c{c} formula under volatility uncertainty in presence of a linear term in the PDE due to discounting. We state our result under different hypothesis with respect to the derivation given by Hu, Ji, Peng and Song (Comparison theorem, Feynman-Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion, Stochastic Processes and their Application, 124 (2)), where the Lipschitz continuity of some functionals is assumed which is not necessarily satisfied in our setting. In particular, we show that the $G$-conditional expectation of a discounted payoff is a viscosity solution of a nonlinear PDE. In applications, this permits to calculate such a sublinear expectation in a computationally efficient way.Comment: 34 pages, 3 figure

Estimating extreme cancellation rates in life insurance

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. © 2021 The Authors. Journal of Risk and Insurance published by Wiley Periodicals LLC on behalf of American Risk and Insurance Association

Detecting asset price bubbles using deep learning

In this paper we employ deep learning techniques to detect financial asset bubbles by using observed call option prices. The proposed algorithm is widely applicable and model-independent. We test the accuracy of our methodology in numerical experiments within a wide range of models and apply it to market data of tech stocks in order to assess if asset price bubbles are present. In addition, we provide a theoretical foundation of our approach in the framework of local volatility models. To this purpose, we give a new necessary and sufficient condition for a process with time-dependent local volatility function to be a strict local martingale.Comment: 29 pages, 3 figure

The challenge of FIGO type 3 leiomyomas and infertility: Exploring therapeutic alternatives amidst limited scientific certainties

Uterine leiomyomas (ULs) are non-cancerous tumors composed of smooth muscle cells that develop within the myometrium and represent the most prevalent pathological condition affecting the female genital tract. Despite the volume of available research, many aspects of ULs remain unresolved, making it a "paradoxical disease" where the increase in available scientific literature has not been matched by an increase in solid evidence for clinical management. Fertility stands at the top of the list of clinical issues where the role of ULs is still unclear. The leiomyoma subclassification system, released by the International Federaion of Gynecology and Obstetrics (FIGO) in 2008, introduced a new and more effective way of categorizing uterine fibroids. The aim was to go beyond the traditional classification "subserosal, intramural and submucosal", facilitating a detailed examination of individual ULs impact on the female reproductive system. The "type 3 UL" is a special type of myoma, characterized by its complete myometrial development while encroaching the endometrium. It is a unique "hybrid" between a submucous and an intramural UL, that may exert a detrimental "double hit" mechanism, which is of particular interest in patients wishing pregnancy. To date, no robust evidence is available regarding the management of type 3 ULs. The aim of this narrative review is to provide a comprehensive overview of the physiopathological mechanisms that type 3 UL may exert on fertility, and to present new perspectives that may help us to better understand both the need for and the methods of treating this unique type of fibroid