József Gáll

Forward interest rate curves in discrete time settings driven by random fields

In this paper, we study the term structure of forward interest rates in discrete time settings. We introduce a generalisation of the classical Heath-Jarrow-Morton type models. The forward rates corresponding to different time to maturity values will be equipped with different driving processes. In this way, we use a discrete time random field to drive the forward rates instead of a single process. We assume the existence of a general stochastic (market) discount factor process, which involves market price of risk factors. This way of building the model is motivated by statistical problems, which is the aim of our further studies. Since we are interested only in arbitrage free markets, we derive several sufficient conditions to exclude arbitrage opportunities in the models and we also present examples for the structure of the driving field, in particular, we use Gaussian autoregression fields.

Maximum likelihood estimator of the volatility of forward rates driven by geometric spatial AR sheet

Discrete-time forward interest rate curve models are studied, where the curves are driven by a random field. Under the assumption of no-arbitrage, the maximum likelihood estimator of the volatility parameter is given and its asymptotic behaviour is studied. First, the so-called martingale models are examined, but we will also deal with the general case, where we include the market price of risk in the discount factor.

Limiting connection between discrete and continuous time forward interest rate curve models

We study discrete time Heath–Jarrow–Morton (HJM) type of interest rate curve models, where the forward interest rates – in contrast to the classical HJM models – are driven by a random field. Our main aim is to investigate the relationship between the discrete time forward interest rate curve model and its continuous time counterpart. We derive a general result on the convergence of discrete time models and we give special focus on the nearly unit root spatial autoregression model.

Poly-ź-Glutamic Acid Nanoparticles Based Visible Light-Curable Hydrogel for Biomedical Application

Nanoparticles and hydrogels have gained notable attention as promising potential for fabrication of scaffolds and delivering materials. Visible light-curable systems can allow for the possibility of in situ fabrication and have the advantage of optimal applicability. In this study nanogel was created from methacrylated poly-gamma-glutamic acid nanoparticles by visible (dental blue) light photopolymerization. The average size of the particles was 80źnm by DLS, and the NMR spectra showed that the methacrylation rate was 10%. Polymerization time was 3 minutes, and a stable nanogel with a swelling rate of 110% was formed. The mechanical parameters of the prepared structure (compression stress 0.73źMPa, and Youngźs modulus 0.93źMPa) can be as strong as necessary in a real situation, for example, in the mouth. A retaining effect of the nanogel was found for ampicillin, and the biocompatibility of this system was tested by Alamar Blue proliferation assay, while the cell morphology was examined by fluorescence and laser scanning confocal microscopy. In conclusion, the nanogel can be used for drug delivery, or it can be suitable for a control factor in different systems.

Effect of production system and pruning on Aphis sambuci dynamics over time and on elderberry yield.

In a 2‐year study, elder aphid (Aphis sambuci) dynamics over time and berry yield were evaluated in two production systems (integrated and organic) and in two winter pruning treatments (trees pruned to four and eight scaffolds) in two black elderberry orchards in Hungary. In the organic production system, the first aphid colony was observed 1–2 weeks earlier (late‐March) in both years and locations compared to the integrated programme. The number of aphid colonies then increased until mid‐May in both years, reaching a maximum number of aphid colonies of 11.2 on 100 scaffolds in the integrated production system and of 38.9 in the organic programme. Then, the number of colonies decreased and reached a zero value at mid‐June in the integrated production system and 2 weeks later (early July) in the organic one in both years and locations. First autumn aphid colonies were observed in early September in the integrated production system but 2 weeks earlier (late August) in the organic one in both years and locations. The number of aphid colonies between mid‐April and mid‐June indicated a larger increase on trees pruned to eight scaffolds compared to trees pruned to four scaffolds. Both the total number of aphid colonies and the area under the aphid colony curves (AUACC) were significantly lower (P < 0.001) in the integrated treatments compared with organic ones. Across all treatments, both measures were significantly lower (P < 0.05) on trees pruned to four scaffolds compared with trees pruned to eight scaffolds. However, when the effect of pruning on the number of aphid colonies was analysed separately for integrated and organic plots, pruning caused significant differences in aphid colony numbers and AUACC in the organic plots. Berry yield was significantly higher (P < 0.05) in the integrated treatments compared with the organic ones, but pruning showed no significant effect on yield. Overall, pruning to four scaffolds resulted in a lower aphid colony number in the organic production system compared to the integrated one. Thus, winter pruning may be useful as an aphid control strategy in organic elderberry orchards.