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This article explores the use of lattice-based approximation schemes for pricing and hedging financial derivatives under GARCH models. The explosion problem and the computational cost associated with the implementation of GARCH-based trees have been well documented in the literature. To address these shortcomings, the authors propose a truncated mean-tracking tree that limits the number of nodes generated within the tree, focusing only on the relevant state space of the GARCH model. The authors assess the efficiency and accuracy of their approach by computing European style option prices and optimal quadratic hedges derived based on the local-risk minimization criteria under the physical measure. The authors test the effectiveness of their approach relative to the standard mean-tracking tree benchmark using different sets of GARCH parameters. Overall, the authors find that their truncation strategy significantly reduces the computational cost of implementing the tree, without sacrificing its accuracy, the largest gains being noticed for longer-term maturity contracts. [ABSTRACT FROM AUTHOR]

In this article, we investigate the pricing and convergence of general non-affine non-Gaussian GARCH-based discretely sampled variance swaps. Explicit solutions for fair strike prices under two different sampling schemes are derived using the extended Girsanov principle as the pricing kernel candidate. Following standard assumptions on time-varying GARCH parameters, we show that these quantities converge respectively to fair strikes of discretely and continuously sampled variance swaps that are constructed based on the weak diffusion limit of the underlying GARCH model. An empirical study which relies on a joint estimation using both historical returns and VIX data indicates that an asymmetric heavier tailed distribution is more appropriate for modelling the GARCH innovations. Finally, we provide several numerical exercises to support our theoretical convergence results in which we further investigate the effect of the quadratic variation approximation for the realized variance, as well as the impact of discrete versus continuous-time modelling of asset returns. [ABSTRACT FROM AUTHOR]

Această lucrare și-a propus să realizeze sinteza studiului materialului ceramic romano-bizantin din Dobrogea publicat de la Vasile Pârvan până în anul 2009, reflectând stadiul actual al publicării acestei categorii de material, reunind aproximativ 3000 de fragmente ceramice. Pornind de la această realitate, şi în lipsa analizelor de pastă, este clar că nu putem vorbi de concluzii definitive şi că acestea vor suferi modificări pe măsură ce vor fi publicate alte loturi ceramice. Prin publicarea concluziilor lucrării de doctorat Ceramica romană din secolul al VI-lea la Dunărea de Jos. Studiu statistic şi funcţional cu vedere specială asupra Dobrogei, aflată la rândul ei în curs de publicare, am dorit să facilităm accesul online la baza de date care a constituit suportul demersului în cauză: (https://cercetari-arheologice.ro/materials/ca28.2.13/CEROM.zip).

Quantifying economic capital and optimally allocating it into portfolios of financial instruments are two key topics in the asset-liability management of an insurance company. In general, these problems are studied in the literature by minimizing standard risk measures such as the value at risk and the conditional VaR. Motivated by Solvency II regulations, we introduce a novel optimization problem to solve for the optimal required capital and the portfolio structure simultaneously, when the ruin probability is used as an insurance solvency constraint. Besides the generic optimal required capital and portfolio problem formulation, we propose a two-model hierarchy of optimization models, where both models admit the so-called second-order conic reformulation, in turn making them particularly well suited for numerics. The first model, albeit naively asserting the normality of the returns on assets and liabilities, under minor further simplifications admits a closed-form solution--a set of formulas, which may be used as simple decision-making guidelines in the analysis of more complex scenarios. A potentially more realistic second model aims to represent the 'heavy-tailed' nature of an insurer's liabilities more accurately, while also allowing arbitrary distributions of asset returns via a semi-parametric approach. Extensive numerical simulations illustrate the sensitivity and robustness of the proposed approach relative to the model's parameters. In addition, we explore the potential of insurance risk diversification and discuss if combining several liabilities into a single insurance portfolio may always be beneficial for the insurer. Finally, we propose an extension of the model with an expected return on capital constraint added. [ABSTRACT FROM AUTHOR]