Multivariate L\'evy Models: Calibration and Pricing

The goal of this paper is to investigate how the marginal and dependence structures of a variety of multivariate L\'evy models affect calibration and pricing. To this aim, we study the approaches of Luciano and Semeraro (2010) and Ballotta and Bonfiglioli (2016) to construct multivariate processes. We explore several calibration methods that can be used to fine-tune the models, and that deal with the observed trade-off between marginal and correlation fit. We carry out a thorough empirical analysis to evaluate the ability of the models to fit market data, price exotic derivatives, and embed a rich dependence structure. By merging theoretical aspects with the results of the empirical test, we provide tools to make suitable decisions about the models and calibration techniques to employ in a real context

Inventory management of vertically differentiated perishable products with stock-out based substitution

The need for optimal inventory control strategies for perishable items is of the utmost importance to reduce the large share of food products that expire before consumption and to achieve responsible food stocking policies. Our study allows for a multi-item setting with substitution between similar goods, deterministic deterioration, delivery lead times and seasonality. Namely, we model demand by a linear discrete choice model to represent a vertical differentiation between products. The verticality assumption is further applied in a novel way within product categories. Specifically, the same product typology is vertically decomposed according to the age of the single stock-keeping unit in a quality-based manner. We compare two different policies to select the daily size of the orders for each product. On the one hand, we apply one of the most classical approaches in inventory management, relying on the Order-Up-To policy, modified to deal with the seasonality. On the other hand, we operate a state-of-the-art actor-critic technique: Soft Actor-Critic (SAC). Although similar in terms of performance, the two policies show diverse replenishment patterns, handling products differently

Data-driven control of a Pendulum Wave Energy Converter: A Gaussian Process Regression approach

The energy coming from the motion of the waves of seas and oceans could be an important component in the solution of the energy problem related to the pursuit of alternatives to fossil fuels. However, wave energy is still technologically immature and it has not reached the economic feasibility required for economy of scale. One of the major technological challenges for the achievement of this goal is the development of control strategies capable of maximizing the extracted energy, adapting to the conditions of the seas and oceans that surround the Wave Energy Converter (WEC) devices. To perform this task, control systems often adopt explicitly control-oriented models, that are by nature affected by uncertainties. On the contrary, to address the problem a data-driven solution is proposed here. The presented strategy applies an optimization approach based on a Gaussian Process Regression (GPR) metamodel to learn the control strategy to be applied. In order to accelerate the learning process, we present a novel method that exploits in the initial phase a previous knowledge given by simulations with the system model and based on the co-kriging concept. To test this approach the Pendulum Wave Energy Converter has been adopted as a case study. To differentiate the previous knowledge and the real system behaviour, a simplified linear model is used to obtain the prior knowledge, while a complex nonlinear one acts as the environment in which simulate the behaviour of the real system. A month-long simulation is used to validate the effectiveness of the proposed strategy, showing the ability of adapting to a real system different from the simplified model on the basis only of data, and overcoming the model-based strategy in terms of performance

Reinforcement learning approaches for the stochastic discrete lot-sizing problem on parallel machines

This paper addresses the stochastic discrete lot-sizing problem on parallel machines, which is a computationally challenging problem also for relatively small instances. We propose two heuristics to deal with it by leveraging reinforcement learning. In particular, we propose a technique based on approximate value iteration around post-decision state variables and one based on multi-agent reinforcement learning. We compare these two approaches with other reinforcement learning methods and more classical solution techniques, showing their effectiveness in addressing realistic size instances

NPM1 Deletion Is Associated with Gross Chromosomal Rearrangements in Leukemia

BACKGROUND: NPM1 gene at chromosome 5q35 is involved in recurrent translocations in leukemia and lymphoma. It also undergoes mutations in 60% of adult acute myeloid leukemia (AML) cases with normal karyotype. The incidence and significance of NPM1 deletion in human leukemia have not been elucidated. METHODOLOGY AND PRINCIPAL FINDINGS: Bone marrow samples from 145 patients with myelodysplastic syndromes (MDS) and AML were included in this study. Cytogenetically 43 cases had isolated 5q-, 84 cases had 5q- plus other changes and 18 cases had complex karyotype without 5q deletion. FISH and direct sequencing investigated the NPM1 gene. NPM1 deletion was an uncommon event in the "5q- syndrome" but occurred in over 40% of cases with high risk MDS/AML with complex karyotypes and 5q loss. It originated from large 5q chromosome deletions. Simultaneous exon 12 mutations were never found. NPM1 gene status was related to the pattern of complex cytogenetic aberrations. NPM1 haploinsufficiency was significantly associated with monosomies (p<0.001) and gross chromosomal rearrangements, i.e., markers, rings, and double minutes (p<0.001), while NPM1 disomy was associated with structural changes (p=0.013). Interestingly, in complex karyotypes with 5q- TP53 deletion and/or mutations are not specifically associated with NPM1 deletion. CONCLUSIONS AND SIGNIFICANCE: NPM1/5q35 deletion is a consistent event in MDS/AML with a 5q-/-5 in complex karyotypes. NPM1 deletion and NPM1 exon 12 mutations appear to be mutually exclusive and are associated with two distinct cytogenetic subsets of MDS and AML

Numerical methods in finance and economics: A MATLAB-based introduction (Chinese edition)

This is the Chinese edition of the original book published by Wiley in 2006. The book deals with numerical methods relevant for financial applications, such as portfolio optimization and derivative pricing. After introductory chapters on financial markets and instruments, also covering models based on stochastic differential equations and risk measurement issues, and on numerical methods, we move on to describe the most important tools, such as: 1) numerical integration by Monte Carlo sampling and low-discrepancy sequences (with due emphasis on variance reduction strategies); 2) finite difference methods for partial differential equations; 3) optimization methods. These methods are illustrated, along with MATLAB code, in later chapters describing several applications to option pricing and portfolio optimization. We deal in particular with binomial/trinomial lattices, exotic option pricing by Monte Carlo simulation, finite difference methods for option pricing, portfolio optimization by mixed-integer and stochastic linear programming, and numerical dynamic programming, which is also the foundation of recent methods to price high-dimensional, American-style options