Le‐Yu Chen, E. Oparina, Nattavudh Powdthavee, Sorawoot Srisuma
Econometric analyses in the happiness literature typically use subjective well-being (SWB) data to compare the mean of observed or latent happiness across samples. Recent critiques show that comparing the mean of ordinal data is only valid under strong assumptions that are usually rejected by SWB data. This leads to an open question whether much of the empirical studies in the economics of happiness literature have been futile. In order to salvage some of the prior results and avoid future issues, we suggest regression analysis of SWB (and other ordinal data) should focus on the median rather than the mean. Median comparisons using parametric models such as the ordered probit and logit can be readily carried out using familiar statistical softwares like STATA. We also show a previously assumed impractical task of estimating a semiparametric median ordered-response model is also possible by using a novel constrained mixed integer optimization technique. We use GSS data to show the famous Easterlin Paradox from the happiness literature holds for the US independent of any parametric assumption.
{"title":"Have Econometric Analyses of Happiness Data Been Futile? A Simple Truth About Happiness Scales","authors":"Le‐Yu Chen, E. Oparina, Nattavudh Powdthavee, Sorawoot Srisuma","doi":"10.2139/ssrn.3349935","DOIUrl":"https://doi.org/10.2139/ssrn.3349935","url":null,"abstract":"Econometric analyses in the happiness literature typically use subjective well-being (SWB) data to compare the mean of observed or latent happiness across samples. Recent critiques show that comparing the mean of ordinal data is only valid under strong assumptions that are usually rejected by SWB data. This leads to an open question whether much of the empirical studies in the economics of happiness literature have been futile. In order to salvage some of the prior results and avoid future issues, we suggest regression analysis of SWB (and other ordinal data) should focus on the median rather than the mean. Median comparisons using parametric models such as the ordered probit and logit can be readily carried out using familiar statistical softwares like STATA. We also show a previously assumed impractical task of estimating a semiparametric median ordered-response model is also possible by using a novel constrained mixed integer optimization technique. We use GSS data to show the famous Easterlin Paradox from the happiness literature holds for the US independent of any parametric assumption.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131135456","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}
A fundamental alternative for stochastic optimization problems named focus programming is proposed based on the focus theory of choice. Different from the existing approaches such as chance-constrained programming and two-stage stochastic programming which are based on expected utility theory, focus programming determines the optimal solution according to which solution’s focus (the most salient realization of random vector) is the most preferred. Focus programming models are bilevel programming problems with maximin-type upper and lower level programs which are interesting and challenging. Two equivalent single-level reformulations of the focus programming models have been proposed for the discrete random vector case.
{"title":"Focus Programming: A Fundamental Alternative for Stochastic Optimization Problems","authors":"P. Guo, Xide Zhu","doi":"10.2139/ssrn.3334211","DOIUrl":"https://doi.org/10.2139/ssrn.3334211","url":null,"abstract":"A fundamental alternative for stochastic optimization problems named focus programming is proposed based on the focus theory of choice. Different from the existing approaches such as chance-constrained programming and two-stage stochastic programming which are based on expected utility theory, focus programming determines the optimal solution according to which solution’s focus (the most salient realization of random vector) is the most preferred. Focus programming models are bilevel programming problems with maximin-type upper and lower level programs which are interesting and challenging. Two equivalent single-level reformulations of the focus programming models have been proposed for the discrete random vector case.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122203925","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}
In trying to establish special angle identities using negative integers, the author observed the equations presented below and picked interest in them due to the frequency with which they showed up. Below, we provide solution to both cases of the equation i.e; when the equation is (+ve) or (-ve).
{"title":"On the Solution of the Equation x=(√a+i√a)÷a²","authors":"Joseph Olloh","doi":"10.2139/ssrn.3333414","DOIUrl":"https://doi.org/10.2139/ssrn.3333414","url":null,"abstract":"In trying to establish special angle identities using negative integers, the author observed the equations presented below and picked interest in them due to the frequency with which they showed up. Below, we provide solution to both cases of the equation i.e; when the equation is (+ve) or (-ve).","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126805495","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}
This paper identifies a necessary and sufficient condition for index-wise comparative statics, which can: (i) establish comparative statics of a single decision without solving the entire model and (ii) enable analysis in settings where substitutability among variables otherwise precludes the use of current comparative statics methods. We prove this result with an extended version of lattice theory. By means of an example, we highlight the advantages as well as disadvantages offered by index-wise comparative statics.
{"title":"Index-Wise Comparative Statics","authors":"Caleb M. Koch","doi":"10.2139/ssrn.3177732","DOIUrl":"https://doi.org/10.2139/ssrn.3177732","url":null,"abstract":"This paper identifies a necessary and sufficient condition for index-wise comparative statics, which can: (i) establish comparative statics of a single decision without solving the entire model and (ii) enable analysis in settings where substitutability among variables otherwise precludes the use of current comparative statics methods. We prove this result with an extended version of lattice theory. By means of an example, we highlight the advantages as well as disadvantages offered by index-wise comparative statics.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127104310","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}
To strike the best balance between insurance risk and profit, insurers transfer insurable risk through reinsurance and enhance yield by participating into the financial market. The long-term commitment of insurance contracts makes insurers necessary to consider time-consistent (TC) reinsurance-investment policies. Using the open-loop TC mean-variance (MV) reinsurance-investment framework, we investigate the equilibrium reinsurance-investment problems for the financial market with unbounded random coefficients or, specifically, an unbounded risk premium. We characterize the problem via a backward stochastic differential equation (BSDE) framework. An explicit solution to the equilibrium strategies is derived for a constant risk aversion under a general class of stochastic models, embracing the constant elasticity of variance (CEV) and Ornstein-Uhlenbeck (OU) processes as special cases. For state-dependent risk aversions, the problem is related to the existence of a solution to a quadratic BSDE with unbounded parameters. A semi-closed form solution is derived, up to the solution to a nonlinear partial differential equation. By examining properties of the equilibrium strategies numerically, we find that the reinsurance decision is greatly affected by the market situation under the state-dependent risk aversion case. We prove the uniqueness of equilibrium strategies for both cases.
{"title":"Time-Consistent Mean-Variance Reinsurance-Investment Problems Under Unbounded Random Parameters: BSDE and Uniqueness","authors":"Bing Han, H. Y. Wong","doi":"10.2139/ssrn.3182387","DOIUrl":"https://doi.org/10.2139/ssrn.3182387","url":null,"abstract":"To strike the best balance between insurance risk and profit, insurers transfer insurable risk through reinsurance and enhance yield by participating into the financial market. The long-term commitment of insurance contracts makes insurers necessary to consider time-consistent (TC) reinsurance-investment policies. Using the open-loop TC mean-variance (MV) reinsurance-investment framework, we investigate the equilibrium reinsurance-investment problems for the financial market with unbounded random coefficients or, specifically, an unbounded risk premium. We characterize the problem via a backward stochastic differential equation (BSDE) framework. An explicit solution to the equilibrium strategies is derived for a constant risk aversion under a general class of stochastic models, embracing the constant elasticity of variance (CEV) and Ornstein-Uhlenbeck (OU) processes as special cases. For state-dependent risk aversions, the problem is related to the existence of a solution to a quadratic BSDE with unbounded parameters. A semi-closed form solution is derived, up to the solution to a nonlinear partial differential equation. By examining properties of the equilibrium strategies numerically, we find that the reinsurance decision is greatly affected by the market situation under the state-dependent risk aversion case. We prove the uniqueness of equilibrium strategies for both cases.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132612784","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}
We present a formal theorem of the square root of the Brownian motion. In doing so, we show that this process can be presented as a typical complex random variable. In addition, we introduce the basic properties of this process.
{"title":"A Theorem of the Square Root of the Brownian Motion","authors":"Moawia Alghalith","doi":"10.2139/ssrn.3317530","DOIUrl":"https://doi.org/10.2139/ssrn.3317530","url":null,"abstract":"We present a formal theorem of the square root of the Brownian motion. In doing so, we show that this process can be presented as a typical complex random variable. In addition, we introduce the basic properties of this process.<br> <br>","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122657397","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}
In this chapter, we present recent developments in using the tools of continuous-time Markov chains for the valuation of European and path-dependent financial derivatives. We also survey results on a newly proposed regime switching approximation to stochastic volatility, and stochastic local volatility models. The presented framework is part of an exciting recent stream of literature on numerical option pricing, and offers a new perspective that combines the theory of diffusion processes, Markov chains, and Fourier techniques. It is also elegantly connected to partial differential equation (PDE) approaches.
{"title":"Continuous-Time Markov Chain and Regime Switching Approximations with Applications to Options Pricing","authors":"Zhenyu Cui, J. Kirkby, D. Nguyen","doi":"10.2139/ssrn.3316432","DOIUrl":"https://doi.org/10.2139/ssrn.3316432","url":null,"abstract":"In this chapter, we present recent developments in using the tools of continuous-time Markov chains for the valuation of European and path-dependent financial derivatives. We also survey results on a newly proposed regime switching approximation to stochastic volatility, and stochastic local volatility models. The presented framework is part of an exciting recent stream of literature on numerical option pricing, and offers a new perspective that combines the theory of diffusion processes, Markov chains, and Fourier techniques. It is also elegantly connected to partial differential equation (PDE) approaches.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114728575","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}
The aim of this paper describes the agency theory in mathematics perspective. The facts are the corporate agents have been given authorization to manage the corporation from the owner as a principal party. The corporate agents can be controlled by the contracts designed through compromising or expected result (outcome) from the principal. The contract has been designed to conduct the agents must provide some efforts to principals. Based on this phenomenon, the mathematics can depict the relationship between the principal and agents. Rationally, the agents usually take the opportunity on inability to monitor in details from the agent’s effort by maximizing the agent’s expected utility from information asymmetry.
{"title":"Agency Theory in Mathematics Perspective","authors":"Ardiansyah Rasyid","doi":"10.2139/ssrn.3313323","DOIUrl":"https://doi.org/10.2139/ssrn.3313323","url":null,"abstract":"The aim of this paper describes the agency theory in mathematics perspective. The facts are the corporate agents have been given authorization to manage the corporation from the owner as a principal party. The corporate agents can be controlled by the contracts designed through compromising or expected result (outcome) from the principal. The contract has been designed to conduct the agents must provide some efforts to principals. Based on this phenomenon, the mathematics can depict the relationship between the principal and agents. Rationally, the agents usually take the opportunity on inability to monitor in details from the agent’s effort by maximizing the agent’s expected utility from information asymmetry.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125463723","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}
Heuristics are numerical methods that can solve difficult optimization models, such as models with multiple local optima, or with discontinuities in their objective functions and constraints. We provide a tutorial for using such methods, in which we tackle the classic subset-sum problem. The chapter is hands-on, and all ideas are illustrated through R code. We also show how the ideas of the tutorial can be used in two applications: selecting variables in a regression model, and computing weights for a portfolio of financial assets.
{"title":"Optimization Heuristics: A Tutorial","authors":"Enrico Schumann","doi":"10.2139/ssrn.3391756","DOIUrl":"https://doi.org/10.2139/ssrn.3391756","url":null,"abstract":"Heuristics are numerical methods that can solve difficult optimization models, such as models with multiple local optima, or with discontinuities in their objective functions and constraints. We provide a tutorial for using such methods, in which we tackle the classic subset-sum problem. The chapter is hands-on, and all ideas are illustrated through R code. We also show how the ideas of the tutorial can be used in two applications: selecting variables in a regression model, and computing weights for a portfolio of financial assets.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133598779","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}
A fundamental assumption in most of economic modeling is that people maximize their utility subject to a budget constraint. This, as well as many other economic problems, math- ematically translate into problems of maximization with constraints. A powerful and widely used method to tackle some of these problems is the method of Lagrange multipliers. Yet, the exposition of such method in standard textbooks is rather formal and utilitarian. In this paper we try to present it emphasising the fundamental intuitions behind the method.
{"title":"Intuitive Mathematical Economics Series. Constrained Maximization and the Method of Lagrange Multipliers","authors":"S. Pernice","doi":"10.2139/ssrn.3333448","DOIUrl":"https://doi.org/10.2139/ssrn.3333448","url":null,"abstract":"A fundamental assumption in most of economic modeling is that people maximize their utility subject to a budget constraint. This, as well as many other economic problems, math- ematically translate into problems of maximization with constraints. A powerful and widely used method to tackle some of these problems is the method of Lagrange multipliers. Yet, the exposition of such method in standard textbooks is rather formal and utilitarian. In this paper we try to present it emphasising the fundamental intuitions behind the method.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125620180","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}
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