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Bayesian Estimation of Finite-Horizon Discrete Choice Dynamic Programming Models 有限视界离散选择动态规划模型的贝叶斯估计
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2016-01-18 DOI: 10.2139/ssrn.2837384
Masakazu Ishihara, Andrew T. Ching
{"title":"Bayesian Estimation of Finite-Horizon Discrete Choice Dynamic Programming Models","authors":"Masakazu Ishihara, Andrew T. Ching","doi":"10.2139/ssrn.2837384","DOIUrl":"https://doi.org/10.2139/ssrn.2837384","url":null,"abstract":"We develop a Bayesian Markov chain Monte Carlo (MCMC) algorithm for estimating finite-horizon discrete choice dynamic programming (DDP) models. The proposed algorithm has the potential to reduce the computational burden significantly when some of the state variables are continuous. In a conventional approach to estimating such a finite-horizon DDP model, researchers achieve a reduction in estimation time by evaluating value functions at only a subset of state points and applying an interpolation method to approximate value functions at the remaining state points (e.g., Keane and Wolpin 1994). Although this approach has proven to be effective, the computational burden could still be high if the model has multiple continuous state variables or the number of periods in the time horizon is large. We propose a new estimation algorithm to reduce the computational burden for estimating this class of models. It extends the Bayesian MCMC algorithm for stationary infinite-horizon DDP models proposed by Imai, Jain and Ching (2009) (IJC). In our algorithm, we solve value functions at only one randomly chosen state point per time period, store those partially solved value functions period by period, and approximate expected value functions nonparametrically using the set of those partially solved value functions. We conduct Monte Carlo exercises and show that our algorithm is able to recover the true parameter values well. Finally, similar to IJC, our algorithm allows researchers to incorporate flexible unobserved heterogeneity, which is often computationally infeasible in the conventional two-step estimation approach (e.g., Hotz and Miller 1993; Aguirregabiria and Mira 2002).","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130856776","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: 4
Mathematical Suggestions to the D/L Rain Method D/L雨法的数学建议
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2015-12-15 DOI: 10.2139/ssrn.2729437
P. Nair
{"title":"Mathematical Suggestions to the D/L Rain Method","authors":"P. Nair","doi":"10.2139/ssrn.2729437","DOIUrl":"https://doi.org/10.2139/ssrn.2729437","url":null,"abstract":"This paper presents mathematical suggestions to the most used rain rule, the Duckworth Lewis method in cricket, used for resetting the match score. IPL Sunrisers team's coach Tom Moody, and innumerable cricketers, statisticians are feeling the need for a correction in the method. Nobody has yet come out with a single solution, common to T20 and ODI, feeling that a \"single\" solution is not possible. But this paper easily traces a natural mechanism common to T20 and ODI, namely an \"integer partition\" in the form of \"90n 30\". Further, it reviews and analyzes the various sections of the D/L method employed in cricket, in the light of modular mathematics, congruence and presents great many surprising things and practical solutions for the ICC to consider.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123407716","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
Evolutionary Sequential Monte Carlo Samplers for Change-Point Models 变点模型的演化序贯蒙特卡罗采样器
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2015-09-08 DOI: 10.2139/ssrn.2657734
A. Dufays
{"title":"Evolutionary Sequential Monte Carlo Samplers for Change-Point Models","authors":"A. Dufays","doi":"10.2139/ssrn.2657734","DOIUrl":"https://doi.org/10.2139/ssrn.2657734","url":null,"abstract":"Sequential Monte Carlo (SMC) methods are widely used for non-linear filtering purposes. Nevertheless the SMC scope encompasses wider applications such as estimating static model parameters so much that it is becoming a serious alternative to Markov-Chain Monte-Carlo (MCMC) methods. Not only SMC algorithms draw posterior distributions of static or dynamic parameters but additionally provide an estimate of the marginal likelihood. The tempered and time (TNT) algorithm, developed in the paper, combines (off-line) tempered SMC inference with on-line SMC inference for drawing realizations from many sequential posterior distributions without experiencing a particle degeneracy problem. Furthermore, it introduces a new MCMC rejuvenation step that is generic, automated and well-suited for multi-modal distributions. As this update relies on the wide heuristic optimization literature, numerous extensions are already available. The algorithm is notably appropriate for estimating Change-point models. As an example, we compare Change-point GARCH models through their marginal likelihoods over time.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134340733","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: 11
Concavifying the Quasi-Concave 拟凹的凹化
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2015-08-17 DOI: 10.2139/ssrn.2645925
C. Connell, E. Rasmusen
{"title":"Concavifying the Quasi-Concave","authors":"C. Connell, E. Rasmusen","doi":"10.2139/ssrn.2645925","DOIUrl":"https://doi.org/10.2139/ssrn.2645925","url":null,"abstract":"This is a 1/3 length math version of a previous paper with the same title. We revisit a classic question of Fenchel from 1953: Which quasiconcave functions can be concavified by a monotonic transformation? While many authors have given partial answers under various assumptions, we offer a complete characterization for all quasiconcave functions without a priori assumptions on regularity. In particular, we show that if and only if a real-valued function <i>f</i> is strictly quasiconcave, (except possibly for a flat interval at its maximum) and furthermore belongs to a certain explicitly determined regularity class, there exists a strictly monotonically increasing function<i>g</i> such that <i>gsmallcircle f</i> is strictly concave. Our primary new contribution is determining this precise minimum regularity class. We prove this sharp characterization of quasiconcavity for continuous but possibly nondifferentiable functions whose domain is any Euclidean space or even any arbitrary geodesic metric space. Under the assumption of twice differentiability, we also establish simpler sufficient conditions for concavifiability on arbitrary Riemannian manifolds, which essentially generalizes those given by Kannai in 1977 for the Euclidean case. Lastly we present the approximation result that if a function <i>f</i> is either weakly or strongly quasiconcave then there exists an arbitrarily close strictly concavifiable approximation<i>h</i> to <i>f</i>.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131193017","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: 2
Comparative Analysis of Mathematical Models in Epidemiology - There Adaptation to Explain Herding in Financial Markets 流行病学数学模型的比较分析——解释金融市场羊群效应的适应性
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2015-07-27 DOI: 10.2139/ssrn.2814843
S. Tomar
{"title":"Comparative Analysis of Mathematical Models in Epidemiology - There Adaptation to Explain Herding in Financial Markets","authors":"S. Tomar","doi":"10.2139/ssrn.2814843","DOIUrl":"https://doi.org/10.2139/ssrn.2814843","url":null,"abstract":"There are different approaches in the use of mathematical model to explain the spread of infectious disease. In epidemiological study the models like Cox,B Spline, SIR and Transmission probability are used to explain herding effect. Bulk of the studies shows the use of these models in Epidemiological research. This paper tries to find the rational of choosing particular models. The collected data sample could be left truncated, right truncated, interval censured and similarly the approximation required to fit the dataset in models could be different. This paper tries to find out the appropriate model which can be used to describe herding phenomena in case of financial market. One of the key finding is that it is better to use B spline model due to the present of left truncated data in a stock market crash or in a bank run.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116925226","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
On the Robust Dynkin Game 关于健壮的Dynkin游戏
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2015-06-30 DOI: 10.2139/ssrn.2806552
Erhan Bayraktar, Song Yao
{"title":"On the Robust Dynkin Game","authors":"Erhan Bayraktar, Song Yao","doi":"10.2139/ssrn.2806552","DOIUrl":"https://doi.org/10.2139/ssrn.2806552","url":null,"abstract":"We analyze a robust version of the Dynkin game over a set P of mutually singular probabilities. We first prove that conservative player's lower and upper value coincide (Let us denote the value by $V$). Such a result connects the robust Dynkin game with second-order doubly reflected backward stochastic differential equations. Also, we show that the value process $V$ is a submartingale under an appropriately defined nonlinear expectation up to the first time when $V$ meets the lower payoff process. If the probability set P is weakly compact, one can even find an optimal triplet for the value V0. The mutual singularity of probabilities in P causes major technical difficulties. To deal with them, we use some new methods including two approximations with respect to the set of stopping times.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128978795","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: 17
New Critical Method of Understanding of the Black - Schole Equation 理解Black - Schole方程的新批判方法
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2015-06-27 DOI: 10.2139/ssrn.2623977
M. A. Popov
{"title":"New Critical Method of Understanding of the Black - Schole Equation","authors":"M. A. Popov","doi":"10.2139/ssrn.2623977","DOIUrl":"https://doi.org/10.2139/ssrn.2623977","url":null,"abstract":"Black - Schole equation is considered as an object of critical ethnomathematics.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125654897","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
Dynamics of Order Positions and Related Queues in a Limit Order Book 限价订单簿中订单位置和相关队列的动态
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2015-05-18 DOI: 10.2139/ssrn.2607702
Xin Guo, Zhao Ruan, Lingjiong Zhu
{"title":"Dynamics of Order Positions and Related Queues in a Limit Order Book","authors":"Xin Guo, Zhao Ruan, Lingjiong Zhu","doi":"10.2139/ssrn.2607702","DOIUrl":"https://doi.org/10.2139/ssrn.2607702","url":null,"abstract":"Order positions are key variables in algorithmic trading. This paper studies the limiting behavior of order positions and related queues in a limit order book. In addition to the fluid and diffusion limits for the processes, fluctuations of order positions and related queues around their fluid limits are analyzed. As a corollary, explicit analytical expressions for various quantities of interests in a limit order book are derived.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126702123","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
Single- and Cross-Generation Natural Hedging of Longevity and Financial Risk 寿命与金融风险的单代和跨代自然套期保值
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2015-05-14 DOI: 10.2139/ssrn.2148324
E. Luciano, Luca Regis, Elena Vigna
{"title":"Single- and Cross-Generation Natural Hedging of Longevity and Financial Risk","authors":"E. Luciano, Luca Regis, Elena Vigna","doi":"10.2139/ssrn.2148324","DOIUrl":"https://doi.org/10.2139/ssrn.2148324","url":null,"abstract":"The paper provides natural hedging strategies among death benefits and annuities written on a single and on different generations. It obtains closed-form Delta and Gamma hedges, in the presence of both longevity and interest rate risk. We present an application to UK data on survivorship and bond dynamics. We first compare longevity and financial risk exposures: Deltas and Gammas for longevity risk are greater in absolute value than the corresponding sensitivities for interest rate risk. We then calculate the optimal hedges, both within and across generations. Our results apply to both asset and asset-liability management.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130564599","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: 4
The Forward Smile in Local-Stochastic Volatility Models 局部随机波动率模型的正向微笑
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2015-01-30 DOI: 10.2139/ssrn.2560300
Andrea Mazzon, A. Pascucci
{"title":"The Forward Smile in Local-Stochastic Volatility Models","authors":"Andrea Mazzon, A. Pascucci","doi":"10.2139/ssrn.2560300","DOIUrl":"https://doi.org/10.2139/ssrn.2560300","url":null,"abstract":"We introduce an asymptotic expansion for forward start options in a multi-factor local-stochastic volatility model. We derive explicit approximation formulas for the so-called forward implied volatility which can be useful to price complex path-dependent options, as cliquets. The expansion involves only polynomials and can be computed without the need for numerical procedures or special functions. Recent results on the exploding behaviour of the forward smile in the Heston model are confirmed and generalized to a wider class of local-stochastic volatility models. We illustrate the effectiveness of the technique through some numerical tests. Mathematica codes are freely available on the authors' website.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114969676","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
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