Mathematics eJournal最新文献_第10页

Valuation of a Early Exercise Defined Benefit (DB) Underpin Hybrid Pension Benefit 基于混合养老金福利的早期行使固定收益(DB)的估值

Mathematics eJournal Pub Date : 2017-12-15 DOI: 10.2139/ssrn.3088728

X. Zhu, M. Hardy, D. Saunders

{"title":"Valuation of a Early Exercise Defined Benefit (DB) Underpin Hybrid Pension Benefit","authors":"X. Zhu, M. Hardy, D. Saunders","doi":"10.2139/ssrn.3088728","DOIUrl":"https://doi.org/10.2139/ssrn.3088728","url":null,"abstract":"In this paper we consider three types of embedded options in pension benefit design. The first is the Florida second election (FSE) option, which has been offered to public employees in the state of Florida since 2002. The state runs both defined contribution (DC) and defined benefit (DB) pension plans. Employees who initially join the DC plan have the option to convert to the (DB) plan at a time of their choosing. The cost of the switch is assessed in terms of the ABO (Accrued Benefit Obligation), which is the expected present value of the accrued DB pension at the time of the switch. If the ABO is greater than the DC account, the employee is required to fund the difference. The second is the DB Underpin option, also known as a floor offset plan, under which the employee participates in a DC plan, but with a guaranteed minimum benefit based on a traditional DB formula. The third option can be considered a variation on each of the first two. We remove the requirement from the FSE option for employees to fund any shortfall at the switching date. The resulting plan is similar to the DB underpin, but with the possibility of early exercise. We adopt an arbitrage-free pricing methodology to value each option. We analyse and value the optimal switching strategy for the employee by constructing an exercise frontier, and we illustrate numerically the difference between the FSE, DB Underpin and Early Exercise DB Underpin options.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126089430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Policy Iteration Algorithm for Nonzero-Sum Stochastic Impulse Games 非零和随机脉冲对策的策略迭代算法

Mathematics eJournal Pub Date : 2017-12-01 DOI: 10.1051/PROC/201965027

R. Aïd, Francisco Bernal, M. Mnif, Diego Zabaljauregui, J. Zubelli

引用次数: 4

A Practical Guide to Market Risk Model Validations (Part II - VaR Estimation) 市场风险模型验证实用指南(第二部分- VaR估计)

Mathematics eJournal Pub Date : 2017-11-30 DOI: 10.2139/ssrn.3080557

V. Abramov, M. K. Khan

{"title":"A Practical Guide to Market Risk Model Validations (Part II - VaR Estimation)","authors":"V. Abramov, M. K. Khan","doi":"10.2139/ssrn.3080557","DOIUrl":"https://doi.org/10.2139/ssrn.3080557","url":null,"abstract":"The VaR (Value at Risk) concept has emerged back in 1994 when JP Morgan started routinely using it in its daily reporting. Simply said, it represents a lower bound of large rare losses. The VaR metric became an industry standard for measuring market risk because it is intuitive and easy to interpret. This led to the adaptation of VaR for market risk capital calculations in the 1996 market risk amendment (also know as Basel II). Following the failure of this capitalization approach during the 2008 financial crisis, Basel Committee strengthened capital requirements by introducing stressed VaR (in Basel 2.5) and tail VaR (in Fundamental Review of the Trading Book) metrics. The VaR process involves a number of steps that include input processing, curve building, pricing, hedging, risk factor identification, simulation, and VaR estimation. In this paper, we will focus on the VaR estimation only. All VaR estimation models can be categorized by their simulation technique, simulation object and revaluation methodology. We will define a broad validation framework that includes assessment of the conceptual soundness and performance of various VaR models. Common modeling issues and practical solutions will be discussed as well.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133627486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Fluctuation Identities with Continuous Monitoring and Their Application to Price Barrier Options 连续监测的波动恒等式及其在价格障碍期权中的应用

Mathematics eJournal Pub Date : 2017-11-30 DOI: 10.2139/ssrn.3080495

Carolyn E. Phelan, D. Marazzina, Gianluca Fusai, G. Germano

{"title":"Fluctuation Identities with Continuous Monitoring and Their Application to Price Barrier Options","authors":"Carolyn E. Phelan, D. Marazzina, Gianluca Fusai, G. Germano","doi":"10.2139/ssrn.3080495","DOIUrl":"https://doi.org/10.2139/ssrn.3080495","url":null,"abstract":"We present a numerical scheme to calculate fluctuation identities for exponential L'evy processes in the continuous monitoring case. This includes the Spitzer identities for touching a single upper or lower barrier, and the more difficult case of the two-barriers exit problem. These identities are given in the Fourier-Laplace domain and require numerical inverse transforms. Thus we cover a gap in the literature that has mainly studied the discrete monitoring case; indeed, there are no existing numerical methods that deal with the continuous case. As a motivating application we price continuously monitored barrier options with the underlying asset modelled by an exponential L'evy process. We perform a detailed error analysis of the method and develop error bounds to show how the performance is limited by the truncation error of the sinc-based fast Hilbert transform used for the Wiener-Hopf factorisation. By comparing the results for our new technique with those for the discretely monitored case (which is in the Fourier-$z$ domain) as the monitoring time step approaches zero, we show that the error convergence with continuous monitoring represents a limit for the discretely monitored scheme.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"177 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134159058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Asymptotic Analysis for Spectral Risk Measures Parameterized by Confidence Level 置信水平参数化谱风险测度的渐近分析

Mathematics eJournal Pub Date : 2017-11-20 DOI: 10.4236/jmf.2018.81015

Takashi Kato

引用次数: 0

The Mathematics of Symbols: A Closer Confrontation of the Chinese Cultural Command over Calculations 符号的数学:中国文化对计算的控制的更近的对抗

Mathematics eJournal Pub Date : 2017-10-27 DOI: 10.2139/ssrn.3060522

R. Kashyap

{"title":"The Mathematics of Symbols: A Closer Confrontation of the Chinese Cultural Command over Calculations","authors":"R. Kashyap","doi":"10.2139/ssrn.3060522","DOIUrl":"https://doi.org/10.2139/ssrn.3060522","url":null,"abstract":"Inspired by Malcolm Gladwell’s phenomenal book, Outliers, which talks about the possibility of paddy fields being the perfect place to cultivate mathematics into our genes, we consider an unintended yet welcome consequence of having numerous characters in a writing script (1, 2), towards developing a talent for symbolic manipulation, which is necessary for abstract numerical aptitude. We wish to test the hypothesis that, this introduction from an early age, to many different symbols, provides a cultural advantage, that can be useful for dealing with mathematical symbols and notation. Mathematics is perhaps, the most simple, beautiful and precise language, provided that, we are not flustered by the notation and the strange, somewhat scary characters, that pop out at us, when we are looking at advanced books on Mathematics. Mathematics is simple, because we can only move from one step to the next, based on well established rules (either assumptions or axioms or other rules derived from these foundational rules, termed lemmas or theorems). When the steps are left out, that is when chaos begin to reign. A culture that teaches us not to get bothered, when we see new symbols is perhaps the training we need to deal with Mathematics. Whenever new symbols jump out at us, we just need to add them to our vocabulary, understand the context and proceed further. This is easier said than done, no doubt. But it will definitely not become easier, if we veer away from looking at the new symbols and stop working on becoming accustomed to them.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115902766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

A Binomial Tail Inequality for Successes 成功的二项式尾不等式

Mathematics eJournal Pub Date : 2017-10-23 DOI: 10.2139/ssrn.3057444

Greg Leo

引用次数: 0

Generalized Linear Mixed Models for Dependent Compound Risk Models 相关复合风险模型的广义线性混合模型

Mathematics eJournal Pub Date : 2017-09-29 DOI: 10.2139/ssrn.3045360

Himchan Jeong, Emiliano A. Valdez, Jae Youn Ahn, S. Park

{"title":"Generalized Linear Mixed Models for Dependent Compound Risk Models","authors":"Himchan Jeong, Emiliano A. Valdez, Jae Youn Ahn, S. Park","doi":"10.2139/ssrn.3045360","DOIUrl":"https://doi.org/10.2139/ssrn.3045360","url":null,"abstract":"In ratemaking, calculation of a pure premium has traditionally been based on modeling frequency and severity in an aggregated claims model. For simplicity, it has been a standard practice to assume the independence of loss frequency and loss severity. In recent years, there is sporadic interest in the actuarial literature exploring models that departs from this independence. In this article, we extend the work of Garrido et al. (2016) which uses generalized linear models (GLMs) that account for dependence between frequency and severity and simultaneously incorporate rating factors to capture policyholder heterogeneity. In addition, we quantify and explain the contribution of the variability of claims among policyholders through the use of random effects using generalized linear mixed models (GLMMs). We calibrated our model using a portfolio of auto insurance contracts from a Singapore insurer where we observed claim counts and amounts from policyholders for a period of six years. We compared our results with the dependent GLM considered by Garrido et al. (2016), Tweedie models, and the case of independence. The dependent GLMM shows statistical evidence of positive dependence between frequency and severity. Using validation procedures, we find that the results demonstrate a more superior model when random effects are considered within a GLMM framework.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128214422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 18

Supplier Selection Using Combinative Distance-Based Assessment (CODAS) Method for Multi-Criteria Decision-Making 基于组合距离评估(CODAS)的多准则决策供应商选择

Mathematics eJournal Pub Date : 2017-09-28 DOI: 10.2139/ssrn.3177276

I. Badi, Ali Shetwan, Ali M. Abdulshahed

引用次数: 14

Weighted Risk Capital Allocations in the Presence of Systematic Risk 存在系统风险时的加权风险资本配置

Mathematics eJournal Pub Date : 2017-09-16 DOI: 10.2139/ssrn.3038297

Edward Furman, A. Kuznetsov, R. Zitikis

引用次数: 17