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Credit Risk, Liquidity, and Bubbles 信用风险、流动性和泡沫
Mathematics eJournal Pub Date : 2018-05-28 DOI: 10.2139/ssrn.3191446
R. Jarrow, P. Protter
{"title":"Credit Risk, Liquidity, and Bubbles","authors":"R. Jarrow, P. Protter","doi":"10.2139/ssrn.3191446","DOIUrl":"https://doi.org/10.2139/ssrn.3191446","url":null,"abstract":"This paper presents an arbitrage-free valuation model for a credit risky security where credit risk coexists and interacts with an asset price bubble and liquidity risk (or liquidity costs). As an illustration, this model is applied to determine the fair rate for microfinance loans.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117349006","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
How Sensitive are VAR Forecasts to Prior Hyperparameters? An Automated Sensitivity Analysis VAR预测对先验超参数有多敏感?自动灵敏度分析
Mathematics eJournal Pub Date : 2018-05-28 DOI: 10.2139/ssrn.3185915
J. Chan, Liana Jacobi, Dan Zhu
{"title":"How Sensitive are VAR Forecasts to Prior Hyperparameters? An Automated Sensitivity Analysis","authors":"J. Chan, Liana Jacobi, Dan Zhu","doi":"10.2139/ssrn.3185915","DOIUrl":"https://doi.org/10.2139/ssrn.3185915","url":null,"abstract":"Vector autoregressions (VAR) combined with Minnesota-type priors are widely used for macroeconomic forecasting. The fact that strong but sensible priors can substantially improve forecast performance implies VAR forecasts are sensitive to prior hyperparameters. But the nature of this sensitivity is seldom investigated. We develop a general method based on Automatic Differentiation to systematically compute the sensitivities of forecasts – both points and intervals – with respect to any prior hyperparameters. In a forecasting exercise using US data, we find that forecasts are relatively sensitive to the strength of shrinkage for the VAR coefficients, but they are not much affected by the prior mean of the error covariance matrix or the strength of shrinkage for the intercepts.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122120444","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: 5
Option Valuation Formula for General Garch-in-Mean Models 一般Garch-in-Mean模型的期权估值公式
Mathematics eJournal Pub Date : 2018-05-28 DOI: 10.2139/ssrn.3185994
Z. Qian, Xingcheng Xu
{"title":"Option Valuation Formula for General Garch-in-Mean Models","authors":"Z. Qian, Xingcheng Xu","doi":"10.2139/ssrn.3185994","DOIUrl":"https://doi.org/10.2139/ssrn.3185994","url":null,"abstract":"We derive option pricing formulas based on general GARCH-M models by using risk-neutral arguments. These formulas are beautiful in nature and realistic for applications. We propose a parameter estimation procedure and employ Monte Carlo method to evaluate the price. Demonstrations of these formulas applying to S&P 500 index options are shown. Empirical evidence suggests that both in U.S. stock market and Chinese financial market the performances of these theoretical pricing formulas are better than the results via Black-Scholes' pricing formula with constant volatility.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123169053","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 Sparse Learning Approach to Relative-Volatility-Managed Portfolio Selection 相对波动管理投资组合选择的稀疏学习方法
Mathematics eJournal Pub Date : 2018-05-16 DOI: 10.2139/ssrn.3179569
Chi Seng Pun
{"title":"A Sparse Learning Approach to Relative-Volatility-Managed Portfolio Selection","authors":"Chi Seng Pun","doi":"10.2139/ssrn.3179569","DOIUrl":"https://doi.org/10.2139/ssrn.3179569","url":null,"abstract":"This paper proposes a self-calibrated sparse learning approach for estimating a sparse target vector, which is a product of a precision matrix and a vector, and investigates its application to finance to provide an innovative construction of relative-volatility-managed portfolio (RVMP). The proposed iterative algorithm, called DECODE, jointly estimates a performance measure of the market and the effective parameter vector in the optimal portfolio solution, where the relative-volatility timing is introduced into the risk exposure of an efficient portfolio via the control of its sparsity. The portfolio's risk exposure level, which is linked to its sparsity in the proposed framework, is automatically tuned with the latest market condition without using cross-validation. The algorithm is efficient as it costs only a few computations of quadratic programming. We prove that the iterative algorithm converges and show the oracle inequalities of the DECODE, which provide sufficient conditions for a consistent estimate of an optimal portfolio. The algorithm can also handle the curse of dimensionality that the number of training samples is less than the number of assets. Our empirical studies of over-12-year backtest illustrate the relative-volatility timing feature of the DECODE and the superior out-of-sample performance of the DECODE strategy, which beats the equally-weighted strategy and improves over the shrinkage strategy.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129402496","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
School Choice with Asymmetric Information: Priority Design and the Curse of Acceptance 信息不对称的择校:优先设计与接受诅咒
Mathematics eJournal Pub Date : 2018-05-04 DOI: 10.2139/ssrn.3094384
Andrew Kloosterman, Peter Troyan
{"title":"School Choice with Asymmetric Information: Priority Design and the Curse of Acceptance","authors":"Andrew Kloosterman, Peter Troyan","doi":"10.2139/ssrn.3094384","DOIUrl":"https://doi.org/10.2139/ssrn.3094384","url":null,"abstract":"We generalize standard school choice models to allow for interdependent preferences and differentially informed students. We show that, in general, the commonly used deferred acceptance mechanism is no longer strategy‐proof, the outcome is not stable, and may make less informed students worse off. We attribute these results to a \u0000 curse of acceptance. However, we also show that if priorities are designed appropriately, positive results are recovered: equilibrium strategies are simple, the outcome is stable, and less informed students are protected from the curse of acceptance. Our results have implications for the current debate over priority design in school choice.\u0000","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127672357","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: 5
How to Mine Gold Without Digging 如何在不挖掘的情况下开采黄金
Mathematics eJournal Pub Date : 2018-05-02 DOI: 10.2139/ssrn.3172514
Kevin Guo, Tim Leung, Brian Ward
{"title":"How to Mine Gold Without Digging","authors":"Kevin Guo, Tim Leung, Brian Ward","doi":"10.2139/ssrn.3172514","DOIUrl":"https://doi.org/10.2139/ssrn.3172514","url":null,"abstract":"This paper examines the main drivers of the returns of gold miner stocks and ETFs during 2006–2017. We solve a combined optimal control and stopping problem to demonstrate that gold miner equities behave like real options on gold. Inspired by our proposed model, we construct a method to dynamically replicate gold miner stocks using two factors: the spot gold ETF and market equity portfolio. Furthermore, through each firm’s factor loadings on the replicating portfolio, we dynamically infer the firm’s implied leverage parameters of our model using the Kalman Filter. We find that our approach can explain a significant portion of the drivers of firm implied gold leverage. We posit that gold miner companies hold additional real options which help mitigate firm downside volatility, but these real options contribute to lower returns relative to the replicating portfolio when gold returns are positive.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133104494","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
Generalized Arrow-Pratt Theory 广义Arrow-Pratt理论
Mathematics eJournal Pub Date : 2018-04-19 DOI: 10.2139/ssrn.3165631
Sudhir A. Shah
{"title":"Generalized Arrow-Pratt Theory","authors":"Sudhir A. Shah","doi":"10.2139/ssrn.3165631","DOIUrl":"https://doi.org/10.2139/ssrn.3165631","url":null,"abstract":"Given a utility defined on a Hilbert outcome space, we define at each outcome a generalized Arrow-Pratt (GAP) coefficient belonging to the Hilbert space. Comparing the risk aversion of such utilities using their GAP coefficients is equivalent to doing so in terms of other standard, decision-theoretically persuasive, criteria. The resulting GAP theory of risk aversion significantly expands the scope of the classical Arrow-Pratt theory by admitting a large class of risks with vector outcomes. This allows the theory to address risks that are embodied in a significant class of random processes. The GAP theory's implications are studied in five contexts with Hilbert outcome spaces, namely, the theories of portfolio choice, insurance, asset valuation, auctions and moral hazard in teams. We also show a duality between utility functions on Euclidean spaces and GAP coefficients. Finally, we provide a theoretically well-founded and computationally tractable method for estimating the expected GAP coefficient from empirical data.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128588966","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
Unilateral Support Equilibria 单边支持均衡
Mathematics eJournal Pub Date : 2018-03-27 DOI: 10.2139/ssrn.3150237
J. Schouten, P. Borm, R. Hendrickx
{"title":"Unilateral Support Equilibria","authors":"J. Schouten, P. Borm, R. Hendrickx","doi":"10.2139/ssrn.3150237","DOIUrl":"https://doi.org/10.2139/ssrn.3150237","url":null,"abstract":"Abstract The concept of Berge equilibria is based on supportive behavior among the players: each player is supported by the group of all other players. In this paper, we consider individual support rather than group support. The main idea is to introduce individual support relations, modeled by derangements. In a derangement, every player supports exactly one other player and every player is supported by exactly one other player. A unilaterally supportive strategy combination with respect to every possible derangement is called a unilateral support equilibrium. Our main insight is that in a unilateral support equilibrium, every player is supported by every other player individually. This is reflected by the alternative formulation of a unilateral support equilibrium in terms of pay-off functions, instead of using derangements. Moreover, it is shown that every Berge equilibrium is also a unilateral support equilibrium and we provide an example in which there is no Berge equilibrium, while the set of unilateral support equilibria is non-empty. Finally, the relation between the set of unilateral support equilibria and the set of Nash equilibria is explored.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115661656","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: 6
Beyond Godel
Mathematics eJournal Pub Date : 2018-03-23 DOI: 10.2139/ssrn.3147440
C. Wright
{"title":"Beyond Godel","authors":"C. Wright","doi":"10.2139/ssrn.3147440","DOIUrl":"https://doi.org/10.2139/ssrn.3147440","url":null,"abstract":"In this paper, we start by defining the basic predicate systems used by Gödel in his logical constructions for the creation of a system of computable mathematics. We demonstrate how each of these predicates and the primitive recursive functions can be mapped directly into bitcoin script operations. This is then extended to explore the dual stack 2PDA construction within bitcoin. In this paper we use this extension to demonstrate how the integration of these functions across a dual stack push down automata (2PDA) allows us to create a system that is equivalent to a Turing machine and which can hence handle all grammatical constructs that may be processed within a Turing machine. The function and operation of the bitcoin operational codes and the construction of the stacks leads to different operational conditions than a standard Turing machine, however, it is also noted how this differs from a standard modern registered machine in operation. Ignoring stack limitations we can then see that any computable function may be integrated into operation and solution within bitcoin scripts.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127272930","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
Strong and Weak Multivariate First-Order Stochastic Dominance 强和弱多元一阶随机优势
Mathematics eJournal Pub Date : 2018-03-19 DOI: 10.2139/ssrn.3144058
Miloš Kopa, Barbora Petrová
{"title":"Strong and Weak Multivariate First-Order Stochastic Dominance","authors":"Miloš Kopa, Barbora Petrová","doi":"10.2139/ssrn.3144058","DOIUrl":"https://doi.org/10.2139/ssrn.3144058","url":null,"abstract":"In this article we deal with three types of multivariate first-order stochastic dominance which serve for comparing random vectors. The first one is the strongest and it is generated by all non-decreasing multivariate utility functions. The second one, called weak multivariate stochastic dominance is defined by comparison of cumulative distribution functions of considered random vectors. The last one applies the univariate stochastic dominance notion to linear combinations of marginals. We compare these multivariate stochastic dominance relations among each other. Then we present important properties of strong and weak multivariate first-order stochastic dominance, in particular we describe their generators in the sense of von Neumann-Morgenstern utility functions and we explain their relation to joint and marginal distribution functions. Moreover, we discuss formulations of strong multivariate first-order stochastic dominance between random vectors with discrete distributions. Finally, we apply this stochastic dominance relation as a constraint to multivariate and multiperiod portfolio optimization problems.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117016616","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: 5
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