Search results

The main motivation of this paper is to present  the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L²-convergence rate is established.

The authors establish a result concerning the L²-convergence rate of the solution of backward stochastic differential equation with jumps with respect to the Yosida approximation.

The authors carry out a convergence rate of Yosida approximation to the semi-linear backward stochastic differential equation in infinite dimension.

In this paper, the authors present the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L²-convergence rate is established.

The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition.

A weak convergence approach is adopted to establish the Laplace principle, which is same as the large deviation principle in a Polish space. The sufficient condition for any family of solutions to satisfy the Laplace principle formulated by Budhiraja and Dupuis is used in this work.

Freidlin–Wentzell type large deviation principle holds good for the solution processes of the stochastic functional integral equation with nonlocal condition.

The asymptotic exponential decay rate of the solution processes of the considered equation towards its deterministic counterpart can be estimated using the established results.

The purpose of this paper is to show the existence results for adapted solutions of infinite horizon doubly reflected backward stochastic differential equations with jumps. These results are applied to get the existence of an optimal impulse control strategy for an infinite horizon impulse control problem.

The main methods used to achieve the objectives of this paper are the properties of the Snell envelope which reduce the problem of impulse control to the existence of a pair of right continuous left limited processes. Some numerical results are provided to show the main results.

In this paper, the authors found the existence of a couple of processes via the notion of doubly reflected backward stochastic differential equation to prove the existence of an optimal strategy which maximizes the expected profit of a firm in an infinite horizon problem with jumps.

In this paper, the authors found new tools in stochastic analysis. They extend to the infinite horizon case the results of doubly reflected backward stochastic differential equations with jumps. Then the authors prove the existence of processes using Envelope Snell to find an optimal strategy of our control problem.

The purpose of this article is to propose a detailed methodology to estimate, model and incorporate the non-constant volatility onto a numerical tree scheme, to evaluate a real option, using a quadrinomial multiplicative recombination.

This article uses the multiplicative quadrinomial tree numerical method with non-constant volatility, based on stochastic differential equations of the GARCH-diffusion type to value real options when the volatility is stochastic.

Findings showed that in the proposed method with volatility tends to zero, the multiplicative binomial traditional method is a particular case, and results are comparable between these methodologies, as well as to the exact solution offered by the Black–Scholes model.

The originality of this paper lies in try to model the implicit (conditional) market volatility to assess, based on that, a real option using a quadrinomial tree, including into this valuation the stochastic volatility of the underlying asset. The main contribution is the formal derivation of a risk-neutral valuation as well as the market risk premium associated with volatility, verifying this condition via numerical test on simulated and real data, showing that our proposal is consistent with Black and Scholes formula and multiplicative binomial trees method.

This study aims to assess the use of variational quantum imaginary time evolution for solving partial differential equations using real-amplitude ansätze with full circular entangling layers. A graphical mapping technique for encoding impulse functions is also proposed.

The Smoluchowski equation, including the Derjaguin–Landau–Verwey–Overbeek potential energy, is solved to simulate colloidal deposition on a planar wall. The performance of different types of entangling layers and over-parameterization is evaluated.

Colloidal transport can be modelled adequately with variational quantum simulations. Full circular entangling layers with real-amplitude ansätze lead to higher-fidelity solutions. In most cases, the proposed graphical mapping technique requires only a single bit-flip with a parametric gate. Over-parameterization is necessary to satisfy certain physical boundary conditions, and higher-order time-stepping reduces norm errors.

Variational quantum simulation can solve partial differential equations using near-term quantum devices. The proposed graphical mapping technique could potentially aid quantum simulations for certain applications.

This study shows a concrete application of variational quantum simulation methods in solving practically relevant partial differential equations. It also provides insight into the performance of different types of entangling layers and over-parameterization. The proposed graphical mapping technique could be valuable for quantum simulation implementations. The findings contribute to the growing body of research on using variational quantum simulations for solving partial differential equations.

This paper aims to test three parametric models in pricing and hedging higher-order moment swaps. Using vanilla option prices from the volatility surface of the Euro Stoxx 50 Index, the paper shows that the pricing accuracy of these models is very satisfactory under four different pricing error functions. The result is that taking a position in a third moment swap considerably improves the performance of the standard hedge of a variance swap based on a static position in the log-contract and a dynamic trading strategy. The position in the third moment swap is taken by running a Monte Carlo simulation.

This paper undertook empirical tests of three parametric models. The aim of the paper is twofold: assess the pricing accuracy of these models and show how the classical hedge of the variance swap in terms of a position in a log-contract and a dynamic trading strategy can be significantly enhanced by using third-order moment swaps. The pricing accuracy was measured under four different pricing error functions. A Monte Carlo simulation was run to take a position in the third moment swap.

The results of the paper are twofold: the pricing accuracy of the Heston (1993) model and that of two Levy models with stochastic time and stochastic volatility are satisfactory; taking a position in third-order moment swaps can significantly improve the performance of the standard hedge of a variance swap.

The limitation is that these empirical tests are conducted on existing three parametric models. Maybe more critical insights could have been revealed had these tests been conducted in a brand new derivatives pricing model.

This work is 100 per cent original, and it undertook empirical tests of the pricing and hedging accuracy of existing three parametric models.

In this study, the authors introduce a solvability of special type of Langevin differential equations (LDEs) in virtue of geometric function theory. The analytic solutions of the LDEs are considered by utilizing the Caratheodory functions joining the subordination concept. A class of Caratheodory functions involving special functions gives the upper bound solution.

The methodology is based on the geometric function theory.

The authors present a new analytic function for a class of complex LDEs.

The authors introduced a new class of complex differential equation, presented a new technique to indicate the analytic solution and used some special functions.

This survey explores the application of real options theory to the field of health economics. The integration of options theory offers a valuable framework to address these challenges, providing insights into healthcare investments, policy analysis and patient care pathways.

This research employs the real options theory, a financial concept, to delve into health economics challenges. Through a systematic approach, three distinct models rooted in this theory are crafted and analyzed. Firstly, the study examines the value of investing in emerging health technology, factoring in future advantages, associated costs and unpredictability. The second model is patient-centric, evaluating the choice between immediate treatment switch and waiting for more clarity, while also weighing the associated risks. Lastly, the research assesses pandemic-related government policies, emphasizing the importance of delaying decisions in the face of uncertainties, thereby promoting data-driven policymaking.

Three different real options models are presented in this study to illustrate their applicability and value in aiding decision-makers. (1) The first evaluates investments in new technology, analyzing future benefits, discount rates and benefit volatility to determine investment value. (2) In the second model, a patient has the option of switching treatments now or waiting for more information before optimally switching treatments. However, waiting has its risks, such as disease progression. By modeling the potential benefits and risks of both options, and factoring in the time value, this model aids doctors and patients in making informed decisions based on a quantified assessment of potential outcomes. (3) The third model concerns pandemic policy: governments can end or prolong lockdowns. While awaiting more data on the virus might lead to economic and societal strain, the model emphasizes the economic value of deferring decisions under uncertainty.

This research provides a quantified perspective on various decisions in healthcare, from investments in new technology to treatment choices for patients to government decisions regarding pandemics. By applying real options theory, stakeholders can make more evidence-driven decisions.

Decisions about patient care pathways and pandemic policies have direct societal implications. For instance, choices regarding the prolongation or ending of lockdowns can lead to economic and societal strain.

The originality of this study lies in its application of real options theory, a concept from finance, to the realm of health economics, offering novel insights and analytical tools for decision-makers in the healthcare sector.

This study aims to predict overnight stays in Italy at tourist accommodation facilities through a nonlinear, single factor, stochastic model called CIR#. The contribution of this study is twofold: in terms of forecast accuracy and in terms of parsimony (both from the perspective of the data and the complexity of the modeling), especially when a regular pattern in the time series is disrupted. This study shows that the CIR# not only performs better than the considered baseline models but also has a much lower error than other additional models or approaches reported in the literature.

Typically, tourism demand tends to follow regular trends, such as low and high seasons on a quarterly/monthly level and weekends and holidays on a daily level. The data set consists of nights spent in Italy at tourist accommodation establishments as collected on a monthly basis by Eurostat before and during the COVID-19 pandemic breaking regular patterns.

Traditional tourism demand forecasting models may face challenges when massive amounts of search intensity indices are adopted as tourism demand indicators. In addition, given the importance of accurate forecasts, many studies have proposed novel hybrid models or used various combinations of methods. Thus, although there are clear benefits in adopting more complex approaches, the risk is that of dealing with unwieldy models. To demonstrate how this approach can be fruitfully extended to tourism, the accuracy of the CIR# is tested by using standard metrics such as root mean squared errors, mean absolute errors, mean absolute percentage error or average relative mean squared error.

The CIR# model is notably simpler than other models found in literature and does not rely on black box techniques such as those used in neural network (NN) or data science-based models. The carried analysis suggests that the CIR# model outperforms other reference predictions in terms of statistical significance of the error.

The proposed model stands out for being a viable option to the Holt–Winters (HW) model, particularly when dealing with irregular data.

The proposed model has demonstrated superiority even when compared to other models in the literature, and it can be especially useful for tourism stakeholders when making decisions in the presence of disruptions in data patterns.

The novelty lies in the fact that the proposed model is a valid alternative to the HW, especially when the data are not regular. In addition, compared to many existing models in the literature, the CIR# model is notably simpler and more transparent, avoiding the “black box” nature of NN and data science-based models.

一般来说, 旅游需求往往遵循规律的趋势, 例如季度/月的淡季和旺季, 以及日常的周末和假期。该数据集包括欧盟统计局在打破常规模式的2019冠状病毒病大流行之前和期间每月收集的在意大利旅游住宿设施度过的夜晚。

本研究旨在通过一个名为cir#的非线性单因素随机模型来预测意大利游客住宿设施的过夜住宿情况。这项研究的贡献是双重的:在预测准确性方面和在简洁方面(从数据和建模复杂性的角度来看), 特别是当时间序列中的规则模式被打乱时。我们表明, cir#不仅比考虑的基线模型表现更好, 而且比文献中报告的其他模型或方法具有更低的误差。

当大量搜索强度指标被作为旅游需求指标时, 传统的旅游需求预测模型将面临挑战。此外, 鉴于准确预测的重要性, 许多研究提出了新的混合模型或使用各种方法的组合。因此, 尽管采用更复杂的方法有明显的好处, 但风险在于处理难使用的模型。为了证明这种方法能有效地扩展到旅游业, 使用RMSE、MAE、MAPE或AvgReIMSE等标准指标来测试cir#的准确性。

cir#模型明显比文献中发现的其他模型简单, 并且不依赖于黑盒技术, 例如在神经网络或基于数据科学的模型中使用的技术。所进行的分析表明, cir#模型在误差的统计显著性方面优于其他参考预测。

这个模型作为Holt-Winters模型的一个拟议模型, 特别是在处理不规则数据时。

即使与文献中的其他模型相比, 所提出的模型也显示出优越性, 并且在数据模式中断时对旅游利益相关者做出决策特别有用。

创新之处在于所提出的模型是Holt-Winters模型的有效替代方案, 特别是当数据不规律时。此外, 与文献中的许多现有模型相比, cir#模型明显更简单、更透明, 避免了神经网络和基于数据科学的模型的“黑箱”性质。

Normalmente, la demanda turística tiende a seguir tendencias regulares, como temporadas altas y bajas a nivel trimestral/mensual y fines de semana y festivos a nivel diario. El conjunto de datos consiste en las pernoctaciones en Italia en establecimientos de alojamiento turístico recogidas mensualmente por Eurostat antes y durante la pandemia de COVID-19, rompiendo los patrones regulares.

El presente estudio pretende predecir las pernoctaciones en Italia en establecimientos de alojamiento turístico mediante un modelo estocástico no lineal de un solo factor denominado CIR#. La contribución de este estudio es doble: en términos de precisión de la predicción y en términos de parsimonia (tanto desde la perspectiva de los datos como de la complejidad de la modelización), especialmente cuando un patrón regular en la serie temporal se ve interrumpido. Demostramos que el CIR# no sólo aplica mejor que los modelos de referencia considerados, sino que también tiene un error mucho menor que otros modelos o enfoques adicionales de los que se informa en la literatura.

Los modelos tradicionales de previsión de la demanda turística pueden enfrentarse a desafíos cuando se adoptan cantidades masivas de índices de intensidad de búsqueda como indicadores de la demanda turística. Además, dada la importancia de unas previsiones precisas, muchos estudios han propuesto modelos híbridos novedosos o han utilizado diversas combinaciones de métodos. Así pues, aunque la adopción de enfoques más complejos presenta ventajas evidentes, el riesgo es el de enfrentarse a modelos poco manejables. Para demostrar cómo este enfoque puede extenderse de forma fructífera al turismo, se comprueba la precisión del CIR# utilizando métricas estándar como RMSE, MAE, MAPE o AvgReIMSE.

El modelo CIR# es notablemente más sencillo que otros modelos encontrados en la literatura y no se basa en técnicas de caja negra como las utilizadas en los modelos basados en redes neuronales o en la ciencia de datos. El análisis realizado sugiere que el modelo CIR# supera a otras predicciones de referencia en términos de significación estadística del error.

El modelo propuesto destaca por ser una opción viable al modelo Holt-Winters, sobre todo cuando se trata de datos irregulares.

El modelo propuesto ha demostrado su superioridad incluso cuando se compara con otros modelos de la bibliografía, y puede ser especialmente útil para los agentes del sector turístico a la hora de tomar decisiones cuando se producen alteraciones en los patrones de datos.

La novedad radica en que el modelo propuesto es una alternativa válida al Holt-Winters especialmente cuando los datos no son regulares. Además, en comparación con muchos modelos existentes en la literatura, el modelo CIR# es notablemente más sencillo y transparente, evitando la naturaleza de “caja negra” de los modelos basados en redes neuronales y en ciencia de datos.

This study aims to generalize the following result of McDonald and Siegel (1986) on optimal investment: it is optimal for an investor to invest when project cash flows exceed a certain threshold. This study presents other results that refine or extend this one by integrating timing flexibility and changes in cash flows with time-varying transition probabilities for regime switching. This study emphasizes that optimal thresholds are either overvalued or undervalued in the absence of time-varying transition probabilities. Accordingly, the stochastic nature of transition probabilities has important implications to the search for optimal timing of investment.