The explicit Laplace transform for the Wishart process

We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral which extends the original approach of Bru. We compare our methodology with the alternative results given by the variation of constants method, the linearization of the Matrix Riccati ODE's and the Runge-Kutta algorithm. The new formula turns out to be fast and accurate.Comment: Accepted on: Journal of Applied Probability 51(3), 201

An analytic multi-currency model with stochastic volatility and stochastic interest rates

We introduce a tractable multi-currency model with stochastic volatility and correlated stochastic interest rates that takes into account the smile in the FX market and the evolution of yield curves. The pricing of vanilla options on FX rates can be performed effciently through the FFT methodology thanks to the affinity of the model Our framework is also able to describe many non trivial links between FX rates and interest rates: a second calibration exercise highlights the ability of the model to fit simultaneously FX implied volatilities while being coherent with interest rate products

Smiles all around: FX joint calibration in a multi-Heston model

We introduce a novel multi-factor Heston-based stochastic volatility model, which is able to reproduce consistently typical multi-dimensional FX vanilla markets, while retaining the (semi)-analytical tractability typical of affine models and relying on a reasonable number of parameters. A successful joint calibration to real market data is presented together with various in- and out-of-sample calibration exercises to highlight the robustness of the parameters estimation. The proposed model preserves the natural inversion and triangulation symmetries of FX spot rates and its functional form, irrespective of choice of the risk-free currency. That is, all currencies are treated in the same way.Comment: Journal of Banking and Finance. Accepte

A flexible matrix Libor model with smiles

We present a flexible approach for the valuation of interest rate derivatives based on Affine Processes. We extend the methodology proposed in Keller-Ressel et al. (2009) by changing the choice of the state space. We provide semi-closed-form solutions for the pricing of caps and floors. We then show that it is possible to price swaptions in a multifactor setting with a good degree of analytical tractability. This is done via the Edgeworth expansion approach developed in Collin-Dufresne and Goldstein (2002). A numerical exercise illustrates the flexibility of Wishart Libor model in describing the movements of the implied volatility surface

Genetic susceptibility and pharmacogenetics of Multiple Myeloma

Multiple Myeloma (MM) is a hematological neoplasm that represent about 1% of all hematological malignancies. Several evidences have suggested the presence of genetic factor able to confer susceptibility to MM. The study of the role of Single Nucleotide Polymorphisms (SNPs) in MM risk and in MM pharmacogenetics is still lacking of strong associations, although some loci have been shown to affect MM risk. In this context, we performed three different case-control studies on MM susceptibility selecting more than 75 SNPs in genes acting in different pathways relevant for cancer risk. In particular, the role of eight variants in Interleukin-1B (IL1B), Interleukin-2 (IL2), Interleukin-6 (IL6), Tumor Necrosis Factor alpha (TNF-α), Interleukin-1 Receptor 1 (IL1R1), Interleukin-2 receptor beta (IL2RB), Interleukin-6 receptor (IL6R) and TNF receptors superfamily 1 member B (TNFRS1B) genes have been investigated in a case-control study on 202 MM patients and 235 healthy controls. Interestingly, when stratifying the entire populations in two groups by age, genotype at the IL6 locus 597A>G (rs1800797) showed a significantly different distribution between cases and controls in the >60 years stratum. In particular, carriers of the A allele (A/G+A/A) showed a 45% lower risk to develop MM compared to the G/G individuals of the same age strata (OR: 0.55, C.I.: 0.31-0.95, p-value: 0.03). Thus, we can conclude that IL6 could play an age-dependent role in MM susceptibility. Response to treatments, Progression Free Survival (PFS) and Overall Survival (OS) was evaluated in a subset of 91 patients. We found that PFS of patients ≥60 years is influenced by genotype at the TNF-α locus -308G>A (rs1800629). Carriers of the A allele showed a worse PFS, with a 2.5-fold higher risk of progression respect to the patients with G/G genotype. Therefore, in the older group, a higher production of TNF-α, associated with the A allele at the -308G>A (rs1800629) locus, could potentiate the pro-apoptotic effect of TNF-α and result in a better PFS for A carriers. In a second study, we evaluated the impact of SNPs in ATP-Binding Cassette (ABC) superfamily members B1 (ABCB1), G2 (ABCG2), C2 (ABCC2), C1 (ABCC1) and C3 (ABCC3) genes on MM susceptibility in a case control study on 523 cases and 677 controls. Of the 57 SNPs genotyped, three in ABCB1 (rs2214102, rs2235074, rs10276499) and one in ABCG2 (rs2725248) showed a positive association at a conventional p<0.05 with MM risk. When correcting for multiple testing, none of the positive hits found reached the threshold p-value (p<0.001), even if the two ABCB1 SNPs rs2235074 and rs10276499 showed trends close to significance. With the aim to further investigate these associations, we replicated the 4 SNPs in an independent population of 588 MM cases and 1509 controls of German origin. We did not find any statistically significant association if considering the replication population alone. However, analyzing the two sets jointly, we found that ABCB1 SNP rs2235074 showed a statistically significant associations for the trend test with a decreased risk of MM (p=0.018). Therefore, we cannot exclude a role, albeit minor, of ABCB1 polymorphisms in MM risk. Finally, on the same population of 523 MM cases and 677 controls, a third study of variants in Nuclear Receptor 1, Type II (NR1I2 or PXR) and Nuclear Receptor 1, Type III (NR1I3 or CAR) genes have been conducted. Of the 17 SNPs successfully genotyped, three variants in CAR (rs3003596, rs11265571, rs4233368) showed a positive association at a conventional p-value of 0.05 with MM risk. In particular, carriers of the G allele for the rs3003596 showed a 42% increased risk to develop MM when compared with A/A individuals (OR: 1.42, C.I.: 1.09 – 1.85, p=0.009). Thus, we can conclude that CAR could play an important role in MM susceptibility, even if further investigation are needed. We can conclude that our studies covered several well studied genes in relation to different types of cancer, adding a significant gain of knowledge to genetics of MM

Influenza di polimorfismi del gene MDR1 sulla prognosi di pazienti affetti da Mieloma Multiplo

Il mieloma multiplo è una neoplasia ematologica che corrisponde all’1% di tutte le neoplasie maligne ed in particolare il 10% di tutte le neoplasie. In Italia, l’incidenza annua è di 2-4 nuovi casi ogni 100000 individui. La prognosi è solitamente sfavorevole, con una sopravvivenza media che oscilla tra 20 e 60 mesi. Il trattamento del mieloma multiplo è solitamente scelto sulla base della valutazione di parametri clinici e sullo stadio della malattia. Uno dei regimi principali utilizzati è il protocollo DAV, o VAD-like, (Vincristina, Adriamicina, Desametasone), che assicura un buon tasso di risposte senza danneggiare le cellule sane del midollo che sono necessarie per il susseguente trapianto autologo di cellule staminali (ASCT). Questo regime terapeutico è solitamente seguito dal trattamento con ciclofosfamide, allo scopo di mobilizzare le cellule staminali nel sangue periferico, accoppiato alla somministrazione di melphalan ad alte dosi, il quale ha l’obiettivo di eradicare le cellule neoplastiche in preparazione di almeno un ( a volte due) trapianto di cellule staminali, per ripopolare il midollo osseo. Nonostante ciò, molti pazienti ricadono in un tempo variabile dopo il trattamento. La profonda variabilità nella risposta clinica a questo trattamento che è stata osservata potrebbe essere interpretata come il risultato di variazioni genetiche, quali i polimorfismi a singolo nucleotide (SNPs), che possono modificare l’espressione e/o la funzionalità di proteine chiave coinvolte nel meccanismo di azione o nel metabolismo dei farmaci somministrati. E’ comunemente accettato che la localizzazione dei farmaci e la loro disponibilità cellulare può influenzare l’esito di terapie anticancro, quindi nel presente studio abbiamo investigato il possibile effetto di due polimorfismi del gene MDR1 sulla risposta al trattamento e sulla sopravvivenza a ungo termine in pazienti affetti da mieloma multiplo. I due SNPs sono la sostituzione silente C3435T, situata nell’esone 26, e il polimorfismo triallelico G2677T/A, situato nell’esone 21 del gene MDR1, che codifica per la P-Glicoproteina 1, la quale è stata riconosciuta come un importante fattore in grado di influenzare diversi parametri farmacocinetici grazie al suo ruolo nella regolazione dell’assorbimento e della disponibilità di numerosi farmaci non correlati tra loro, molti dei quali sono correntemente utilizzati nella terapia anticancro. Abbiamo analizzato un totale di 110 pazienti aggetti da mieloma multiplo, trattati con DAV seguito fa ASCT. Il DNA è stato estratto da sangue intero e i genotipi degli SNPs C3435T e G2677T/A sono stato ottenuti rispettivamente utilizzando la Real Time PCR con il metodo Taqman e l’analisi dei polimorfismi di lunghezza dei frammenti di restrizione RFLP. I risultati mostrano che non c’è associazione tra nessuno dei due SNPs e la risposta alla terapia. Tuttavia, gli individui omozigoti per l’allele T alla posizione 3435 mostrano un incremento della sopravvivenza a lungo termine statisticamente significativo (log rank test p=0,02). Risultati simili sono stati ottenuti per l’altro polimorfismo, dove è stata osservata un’associazione ai limiti della significatività tra i genotipi T/T e T/A ed una migliore sopravvivenza (log rank test p=0,05) In conclusione, il genotipo al locus MDR1 sembra essere un buon marcatore predittivo per la sopravvivenza a lungo termine in pazienti affetti da mieloma multiplo. Questo è il primo studio che dimostra un ruolo prognostico di MDR1 per il mieloma multiplo, il quale potrebbe avere un ruolo importante nel selezionare l’approccio terapeutico più appropriato in accordo con la struttura genetica di ciascun individuo.

A tree-based kernel for graphs with continuous attributes

The availability of graph data with node attributes that can be either discrete or real-valued is constantly increasing. While existing kernel methods are effective techniques for dealing with graphs having discrete node labels, their adaptation to non-discrete or continuous node attributes has been limited, mainly for computational issues. Recently, a few kernels especially tailored for this domain, and that trade predictive performance for computational efficiency, have been proposed. In this paper, we propose a graph kernel for complex and continuous nodes' attributes, whose features are tree structures extracted from specific graph visits. The kernel manages to keep the same complexity of state-of-the-art kernels while implicitly using a larger feature space. We further present an approximated variant of the kernel which reduces its complexity significantly. Experimental results obtained on six real-world datasets show that the kernel is the best performing one on most of them. Moreover, in most cases the approximated version reaches comparable performances to current state-of-the-art kernels in terms of classification accuracy while greatly shortening the running times.Comment: This work has been submitted to the IEEE Transactions on Neural Networks and Learning Systems for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Mean field games models of segregation

This paper introduces and analyzes some models in the framework of mean field games (MFGs) describing interactions between two populations motivated by the studies on urban settlements and residential choice by Thomas Schelling. For static games, a large population limit is proved. For differential games with noise, the existence of solutions is established for the systems of partial differential equations of MFG theory, in the stationary and in the evolutive case. Numerical methods are proposed with several simulations. In the examples and in the numerical results, particular emphasis is put on the phenomenon of segregation between the populations. </jats:p

An Empirical Study on Budget-Aware Online Kernel Algorithms for Streams of Graphs

Kernel methods are considered an effective technique for on-line learning. Many approaches have been developed for compactly representing the dual solution of a kernel method when the problem imposes memory constraints. However, in literature no work is specifically tailored to streams of graphs. Motivated by the fact that the size of the feature space representation of many state-of-the-art graph kernels is relatively small and thus it is explicitly computable, we study whether executing kernel algorithms in the feature space can be more effective than the classical dual approach. We study three different algorithms and various strategies for managing the budget. Efficiency and efficacy of the proposed approaches are experimentally assessed on relatively large graph streams exhibiting concept drift. It turns out that, when strict memory budget constraints have to be enforced, working in feature space, given the current state of the art on graph kernels, is more than a viable alternative to dual approaches, both in terms of speed and classification performance.Comment: Author's version of the manuscript, to appear in Neurocomputing (ELSEVIER