Compute the logarithm of the softmax function. Explores how system dynamics can help organizations achieve important goals. Fourier coefficients for even Mathieu and modified Mathieu functions. Includes study and discussion of concepts, examples, and case studies from a wide range of industries. gaussian(link = "identity") Focuses on a range of industries, from technology-based firms with global roots to emerging market multinationals. Students examine the critical entrepreneurial and innovation challenges facing entrepreneurs inside new and established firms, and develop frameworks that allow them to identify, evaluate, iterate, and integrate their ideas effectively. Examines downstream issues surrounding the adoption, distribution, and scaling (via business, non-profit, or public policy channels) of new solutions in an international development context. \end{array}\right.\hspace{-5pt}, Design Longitudinal cohort For the final project, students write a short case, record a conversation, and assess their work. More generally, these results indicate substantial differences in the characteristics of firms that experience CDS introduction compared to those that do not. These results show that the interaction between CDS contracts and local bankruptcy codes also influences the investment policies of firms. Provides understanding of the theory and processes of negotiation as practiced in a variety of settings. \left( {1 - \phi } \right)q\lambda C_2^L } \right]& \mbox{if }F_C^L < F \le F_C^H \\ If |$F > F_C^H $|, strategic default would always arise even in the up-up state in our binomial path, and the maximum pledgeable cash flow degenerates to |$\phi q\lambda C_2^H + (1 - \phi )q\lambda C_2^L $|, which is less than the funding the firm would have achieved at |$F = F_C^H $| in Equation (1). Each case has a full width at half-maximum of very nearly 3.6. Includes guest lectures on the practices and tools used in private equity and M&A. Topics may include motivation, decision making, negotiation, power, influence, group dynamics, and leadership. Teams gather evidence that permits a fact-based iteration across multiple application domains, markets, functionalities, technologies, and products, leading to a recommendation that maps a space of opportunity and includes actionable next steps to evolve the market and technology. Covers the micro-foundations of the knowledge production function (including the role of creativity and the impact of Science), the impact of institutions and strategic interaction on the commercialization of new technology, and the diffusion and welfare impact of ideas and technology. Focuses on the CEO and other analogous leadership roles such as co-founder, chairman of the board, etc. Negative binomial cumulative distribution function. Topics: reports of research projects (proposed or in progress) and informal discussions of recent literature dealing with subjects of special interest to participants. Meets with 15.617 when offered concurrently. mu is only available after fit is called. We first estimate the markets propensity to introduce CDSs to firms, using an extensive array of firm and country characteristics, and then use the resultant propensity scores as a weighting mechanism for the sample in our analysis. An intensive introduction to the interpretation of financial information. Despite its name, the first explicit analysis of the properties of the Cauchy distribution was published by the French Covers the process of identifying and quantifying market opportunities, then conceptualizing, planning, and starting a new, technology-based enterprise. Includes an introductory retreat, weekly class sessions, written reflections, interactive exercises, and professional executive coaching to enable students to clarify and articulate their leadership aspirations. Includes team projects. Overall, the results from our extended model highlight that the real effects of CDSs on reference entities depend on features of the home countrys legal environment.2, We conduct our empirical analysis using a sample of more than 56,000 firms from 51 countries during the period 20012015. Calculate degrees of freedom (denominator) for the noncentral F-distribution. Prereq: Permission of instructor G (Spring)3-0-6 units. Subject to availability, some projects may explore policy issues. Adopts a decision-maker perspective of accounting by emphasizing the relation between accounting data and the underlying economic events generating them. All regressions include Fama-French 48-industry fixed effects. Examines how corporations choose securities and markets to finance themselves. Applies current debates on tax policy options and recent tax law changes to class discussions. Prereq: Permission of instructor G (Spring; first half of term) Expectations and evaluation criteria differ for students taking graduate version; consult syllabus or instructor for specific details. Covers topics such as time series forecasting, choice modeling, queuing theory, network models, dynamic programming, mixed-integer programming, stochastic optimization, matching algorithms, multi-armed bandits. Develops an integrated approach to analysis of climate change processes, and assessment of proposed policy measures, drawing on research and model development within the MIT Joint Program on the Science and Policy of Global Change. Prereq: Permission of instructor G (Fall)4-0-5 unitsCredit cannot also be received for 15.511, 15.720. Covers complex valuations, modelling of capital structure decisions, financial restructuring, analysis and modelling of merger transactions, and real options. A single-name CDS contract specifies the underlying reference entity; the maturity of the contract; the ongoing payments that are required to be made by the protection buyer to the protection seller; the definition of the credit events that would trigger an obligation due from the protection seller to the protection buyer; the manner in which the payments from seller to buyer will be determined; and the manner in which the contractual securities may be delivered (physically or otherwise) will be set. for the quasi- families). The use of overlap weights ensures that covariates are perfectly balanced between treated firms and control firms in the year before treatment (see Table E.2 in Appendix E). Centers around a semester-long action learning project in which students assist a local nonprofit organization in improving its efficiency and effectiveness. Expectations and evaluation criteria differ for students taking graduate version; consult syllabus or instructor for specific details. Prereq: None U (IAP)Units arranged [P/D/F]Can be repeated for credit. We provide below a description of the economic intuition behind these parameters and the variables in our data set that best capture these effects. Prereq: 10.807[J] or 15.390 G (Spring; first half of term)3-0-3 units. Provides instruction in tools used in the financial industry to process massive data sets, including SQL, relational and multidimensional databases. Students receive extensive, personalized feedback from teaching team, coaches, and classmates. To calculate overlap weights as described in Section 5, we estimate logit regressions, using an indicator variable for CDS introduction as the dependent variable. HASS-S; CI-H, Same subject as 11.257[J] Not offered regularly; consult department4-0-5 units. Classroom interactions based primarily on case studies. Each session focuses on a specific field of medicine. Survey of basic principles for successfully managing and leading people, particularly in public service and the military. total number of cases given by the weights). Economic and financial considerations of the drug development process. For property rights, we consider the following three measures: Law & Order, Corruption, and Political Risk, where higher index values indicate stronger protection for private properties. Restricted to Executive MBA students. Firm- and country-level characteristics without imposition of overlap weights. = S.Inverse(Xb) The link function defines the relationship f ( ) = X * b between the mean response and the linear combination of predictors X * b . Restricted to Executive MBA and Sloan Fellow MBA students. The coefficient for the interaction term of CDS introduction with Efficiency is negative and significant at the 10|$\%$| level. Its derivative is called the quantile density function. Presents formulations and their connection to probability, information and risk theory for conic optimization (linear, second-order, and semidefinite cones) and integer optimization. Presents analytics algorithms, and their implementations in data science. Specifically, we see coefficients of |$-$|0.129 (|$t$|-statistic |$= -3.1$|) on the Creditor Rights index, and coefficients of |$-$|0.129 (|$t$|-statistic |$= -2.7$|), |$-$|0.310 (|$t-$|statistic |$= -6.1$|) and |$-$|0.129 (|$t$|-statistic |$= -2.6$|) on Restrictions on Entry, No Automatic Stay, and Management Does Not Stay, respectively. 15.390 is recommended as a prerequisite. The use of an international sample provides us with cross-sectional variation in the legal environment, particularly creditor rights, which may influence the effect of the introduction of CDSs. Topics include formulating problems in integer variables, enhancement of formulations, ideal formulations, integer programming duality, linear and semidefinite relaxations, lattices and their applications, the geometry of integer programming, primal methods, cutting plane methods, connections with algebraic geometry, computational complexity, approximation algorithms, heuristic and enumerative algorithms, mixed integer programming and solutions of large-scale problems. Provides practical experience in using tools to identify, evaluate, and develop marketing strategies; design efficient products and selling formats; and plan the use and development of the firm's portfolio of resources. Prereq: None G (Fall, Spring; first half of term)2-0-1 units. \end{array}. For instance, when the local bankruptcy codes allow creditors to limit a firms ability to file for an in-court restructuring that it claims is voluntary, creditors clearly have stronger bargaining power and, in particular, the uncertainty related to triggering events in CDS contracts is reduced. Business applications for use in the next two to seven years, including: e-commerce, marketing, finance, trust/security, health/biomedical, mobile. Preference to students who have taken 15.232. Not offered regularly; consult departmentUnits arrangedCan be repeated for credit. Not offered regularly; consult department3-0-3 unitsCredit cannot also be received for 15.714. L. Caglio, C., Darst R. M., and Parolin E.. Chakraborty, I., Chava S., and Ganduri R.. Christensen, H. B., Hail L., and Leuz C.. Colonnello, S., Efing M., and Zucchi F.. Curtis, L. H., Hammill B. G., and Eisenstein E. L.. Dahlquist, M., Pinkowitz L., Stulz R. M., and Williamson R.. Davydenko, S. A., and Strebulaev I. Focuses on structuring the oral and visual communication of data. Emphasizes the executive perspective: how to leverage best-practice quantitative methods to manage and drive the business. Specific phenomena affecting public companies, such as shareholder activism and passive investing, are also considered. Exposes students to the cutting edge of financial engineering. Restricted to first-year Sloan master's students. Topics include statistical inference, financial time series, event study analysis, and basic machine learning techniques for forecasting. Assignments include a decision analysis paper and a final team project in which students apply their skills to solve a problem in sports. Background readings, regular assignments and active participation by students expected. Introduces principles of microeconomics as a framework for making more informed managerial decisions. Expectations and evaluation criteria differ for students taking graduate version; consult syllabus or instructor for specific details. Also focuses on how global economies will change in light of this wave of technology. Not offered regularly; consult department3-0-6 units. polynomial coefficients is numerically unstable. Topics include machine learning, natural language processing, predictive analytics, regression methods, and time series analysis. Prereq: Permission of instructor G (Fall, Spring)3-0-3 units. Students should have adequate preparation in microeconomic theory and econometrics. function: the variance as a function of the mean. Deep dive into social impact investing -- an approach intentionally seeking to create financial return and positive social impact that is actively measured. Develops communication skills crucial to successful management. Restricted to Executive MBA students. Prepared and taught by veterans in various Sloan programs, under the supervision of MIT Sloan faculty. Emphasizes tools and methods needed to apply systems thinking and simulation modeling successfully in diverse real-world settings, including supply chains, forecasting, project management, process improvement, service operations, and platform-based businesses, among others. Emphasizes the perspective of the general manager in ensuring the firm's success. Also reviews thethree undergraduate majors offered by Sloan as well as careers in management. Standard errors are clustered at the firm level. No listeners; restricted to students in Sloan Entrepreneurship and Innovation (E&I) MBA track. Restricted to MIT Executive MBA and Sloan Fellows students. Covers lead user searches, internet-based crowdsourcing, design by customers using innovation toolkits, and more. input is clamped to [eps, 1 - eps] when eps is not None. The objective of the sensitivity analysis by Ichino, Mealli, and Nannicini (2008) is to assess whether and to what extent the estimated average treatment effects are robust to possible deviations from the conditional independence assumption. See description under subject 11.430[J]. Practical introduction to the process of product management. This uncertainty captures differences in the way that local bankruptcy codes interact with the standardized definitions of CDS contract terms established by the International Swaps and Derivatives Association (ISDA). B_{CDS}^{Empty} = \left\{\hspace{-2pt}\begin{array}{ll} Addresses law-sensitive issues arising in the overlapping contexts of complex deals and financial services and products. Students are assigned to teams, and each team is assigned one such problem. Helps students discover and develop new and effective ways of managing and working together across national borders; also helps accelerate development of the context awareness and integrative management skills needed to lead in a globalized world. Substantial time spent learning how to effectively tell leadership stories and examine leadership identity, drawing on theory from the leadership literature, family systems, developmental psychology, personality psychology, and organizational change. Introduces a wide variety of modern strategy frameworks and methodologies. 23 Given that these regressions include both CDS and non-CDS observations, the total number of firm-year observations of 80,822 in the logit regression in Table 2 (and the subsequent analyses) is much larger than the number of 1,421 CDS introductions reported in Table 1, panel B. The strength of the private credit market is measured by domestic credit extended by financial corporations to the private sector scaled by GDP ( Domestic Credit to Private Sector), and by total credit to the private nonfinancial sector scaled by GDP ( Private Credit), obtained from the World Development Indicators database of the World Bank and BISs Total Credit Statistics, respectively. Acad Year 2023-2024: G (Fall)3-0-6 units. Includes oral presentations and writing assignments with feedback to help students improve their communication effectiveness. In probability theory, an exponentially modified Gaussian distribution (EMG, also known as exGaussian distribution) describes the sum of independent normal and exponential random variables. Doctoral student seminar covering current topics in applied probability and stochastic processes. For more information on the canonical link functions, see Canonical Link Function . \theta \left({1 - \phi } \right)\left( {F - q\lambda C_2^L } \right) + \left( {1 - \theta } \right)\left[ {\phi {\it max}(\gamma N - q\lambda C_2^H,0) + \left( {1 - \phi } \right)(S - q\lambda C_2^L )} \right] &\mbox{if } F \in (F_C^L,\tilde{F}_C^L]\\[6pt] the Gamma family the links inverse, identity In contrast to the significant coefficients on Restrictions on Entry and Secured Creditors First, we find no significant effects on leverage for the interaction of CDS introduction and either No Automatic Stay or Management Does Not Stay. Probability Distributions of Discrete Random Variables. Focuses on the nature of military leadership and its relevance to the civilian professional and organizational experience. In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. Compute x*log1p(y) so that the result is 0 if x = 0. logsumexp(a[,axis,b,keepdims,return_sign]). Standard errors are clustered at the firm level and are reported in parentheses. Draws on materials from the MIT Task Force on Work of the Future and the online course Shaping Work of the Future. Similar in content to 15.311; shares lectures with 15.301. Prereq: None G (Spring)3-0-6 unitsCredit cannot also be received for 15.3941. In weekly coaching circles, each student has one full session to present their current leadership edge and receive feedback from peer coaches. When the enforcement of debt contracts faces significant limited-commitment problems due to a weak institutional environment (low |$\lambda $|, low |$q$|), well-functioning credit derivatives contracts, such as CDSs, can help firms overcome such institutional barriers. Presents examples of successful applications in credit ratings, fraud detection, marketing, customer relationship management, investments, and synthetic clinical trials. 1 - p_{it} \left( {x_t } \right),&for\;Z_{it} = 1\\ Topics chosen from logistic regression; principal components and dimension reduction; discrimination and classification analysis, trees (CART), partial least squares, nearest neighbors, regularized methods, support vector machines, boosting and bagging, clustering, independent component analysis, and nonparametric regression. (2008), which indicates that deviations from absolute priority rules are associated with substantially lower recovery rates. Intensive, project-based subject intended for startup teams already working on building a new, high-impact venture. Generalized Linear Models. Not offered regularly; consult departmentUnits arranged. Addresses key questions that are central to the funding and growth of high-tech start-up firms, such as how to value entrepreneurial firms using different valuation methods, and how to negotiate investor term sheets and convertible notes. Compute zeros of integer-order Bessel function derivatives Jn'. Acad Year 2023-2024: G (Spring)3-0-9 units. Same subject as HST.971[J]Prereq: None G (Spring)3-0-6 units. Cultivates students' ability to respond to the unexpected with confidence and agility. Expectations and evaluation criteria differ for students taking graduate version; consult syllabus or instructor for specific details. Finally, CDS are less (more) likely to be introduced in firms where ownership concentration is high (low); the coefficient on Closely Held Shares is negative and statistically significant (coefficient |$= -0.259$|, |$t$|-statistic |$= -6.3$|). Through models and case studies of successful applications students develop proficiency in how to use qualitative and quantitative data to formulate and test models, and how to work effectively with senior executives to implement change successfully. Same subject as 1.813[J], 11.466[J], IDS.437[J]Prereq: Permission of instructor G (Fall)3-0-9 units. \end{align}$$, $$\begin{align}\frac{\partial \Delta B}{\partial \lambda } &= \left\{ Provides frameworks as well as a range of practical tools to address these goals. logit honors female, or Iteration 0: Magnitudes of positive and negative effects should be compared by taking the inverse of the negative effect, or vice versa. Enrollment by application only. 18 There are other methods of achieving balance in treated and nontreated samples prior to estimating treatment effects; these methods include the use of covariate balancing propensity scores (CBPS) (Imai and Ratkovic 2014) and the use of entropy balancing (see, e.g., Hainmueller 2012). As a consequence, in estimating treatment effects, we estimate the effects of individual conditioning variables related to creditor rights, property rights, and equity ownership concentration, and the interaction effects of these variables with CDS introduction in separate regressions. Discusses the supply and demand paradigm with applications to digital marketplaces, innovation, sources of market power, and strategic pricing. If the protocols are successful in reducing legal uncertainty, then we would expect the coefficient on the interaction effect of CDS introduction and restrictions on entry to be reduced (or, equivalently, we would expect the triple interaction coefficient to be negative). This may indicate a stronger interest in CDS protection in circumstances in which a more dispersed ownership base might be expected to engage in relatively little monitoring. Prereq: 15.002 G (Spring)Units arranged [P/D/F]. Designed to help students understand the fundamental rules and practices of corporate boards in three key areas: the audit committee, the compensation committee, and corporate takeovers. Prereq: None G (Fall; first half of term)3-0-3 units. Topics covered include: structural estimation ofcorporate finance models, financial intermediation, corporate taxation, aggregate effects of financing frictions, corporate finance with irrational managers or irrationalinvestors and entrepreneurial finance (young firm dynamics, venture capital and private equity). Table 1, panel C, reports the number of firms in each industry that have CDS available by year, using the Fama-French 48-industry groupings. Prereq: 15.900 or 15.902 Acad Year 2022-2023: Not offered Also provides an introduction to the main groups that together form the Behavioral Policy Sciences (BPS) area of MIT/Sloan, including economic sociology, organization studies, work and employment, strategic management, global management, and technology, innovation, and entrepreneurship. Multidisciplinary perspective from faculty in clinical; life; and management sciences; as well as industry guests. w_{it} \left( {x_t } \right) = \left\{\begin{array}{ll} Compute nt zeros of the derivative of the Kelvin function bei. - \left( {1 - \theta } \right)\lambda \left[\phi C_2^H 1_{\gamma N > q\lambda C_2^H } + \left( {1 - \phi } \right)C_2^L \right]& \mbox{if }F \le F_C^L \\ Specifically, our results indicate that while the introduction of CDS contracts is associated with higher leverage, this effect is significantly larger when the legal environment provides creditors with greater certainty about their ability to use their (stronger) creditor rights (high |$\gamma $|, proxied by creditors ability to restrict entry into reorganization); with weaker ability to enforce contracts (low |$\lambda $|, proxied by weak property rights); with higher priority in the event of liquidation (high |$S$|, proxied by the payment of liquidation proceeds to secured creditors first); and with weaker initial bargaining power relative to shareholders (low |$q$|, proxied by the extent to which the firm is closely held). Prereq: Permission of instructor G (Spring; second half of term)Units arrangedCan be repeated for credit. Prereq: Permission of instructor G (Spring)3-0-6 unitsCredit cannot also be received for 15.511, 15.515. Topics include demand estimation, process analysis and improvement, facility location and capacity planning, inventory management, and supply chain coordination. In each state, the first term in the square brackets denotes the payoff to CDS creditors if they agree with the firm on debt restructuring, whereas the second term in the square brackets denotes their payoff if they reject the offer from the shareholders and take their case to the DC (or, prior to the Big Bang, the local legal authority). Expectations and evaluation criteria differ for students taking graduate version; consult syllabus or instructor for specific details. Application required; restricted to MIT students. Restricted to Master of Business Analytics students. The exception to this is the case in which secured creditors receive priority in payments from the proceeds of liquidation ( Secured Creditor First). Admission by arrangement with individual faculty member. Prereq: 15.402, 15.414, or 15.415 G (Fall)3-0-6 unitsCredit cannot also be received for 15.4341. Covers adequate power sector regulation and computer-aided electrification planning techniques in detail. Qualifies as an elective for the Sloan Sustainability Certificate. An exGaussian random variable Z may be expressed as Z = X + Y, where X and Y are independent, X is Gaussian with mean and variance 2, and Y is exponential of rate . Considers key strategic concepts and ideas useful for managers and entrepreneurs, especially the distinction between a product versus a platform strategy as well as product versus a service strategy. Emphasizes use of behavioral science research methods to test hypotheses concerning decision-making, group behavior, and organizational behavior. See description under subject 1.UAR[J]. \frac{\partial \Delta B}{\partial q} &= \left\{ Designed for entrepreneurial types interested in the FinTech space, this course presents a unique opportunity to work through the nuts and bolts of developing, investing in or acquiring a FinTech startup. Our results are robust as long as the bargaining power of creditors does not increase after their failure to trigger CDS payments, which seems a plausible assumption. Prereq: 15.809, 15.814, or permission of instructor G (Fall; first half of term)3-0-3 unitsCredit cannot also be received for 15.726. Acad Year 2023-2024: U (Fall; second half of term)2-0-4 units. 2003)determines the share of the continuation value, |$C_{2}$|, available to creditors, with the balance going to shareholders. Restricted to Leaders for Global Operations program students. arithmetic, and lose information of the original orthogonal polynomial. Key conceptual frameworks are linked to applications in a variety of industry and case settings. Specific topics vary from year to year. family is a generic function with methods for classes Cox, D. R. and Snell, E. J. Restricted to Sloan Fellow MBA students. Introduces and utilizes key tactics such as risk pooling and inventory placement, integrated planning and collaboration, and information sharing. Builds upon relevant economic theories and methodologies to analyze the changes in organizations and markets enabled by digital technologies. Similarly, lenders capital ratios and portfolio concentration measures, which also have been used in the literature (see, e.g., Saretto and Tookes 2013; Subrahmanyam, Tang, and Wang 2014; Shan, Tang, and Yan 2016) can be confounded with banking regulations that may also affect the availability of CDSs to borrowers from the same country as the lenders. Acharya, V. V., Drechsler I., and Schnabl P.. Augustin, P., Subrahmanyam M. G., Tang D. Y., and Wang S. Q.. Bartram, S. M., Brown G. W., and Conrad J. Readings from developmental psychology and leadership literature augment analyses. Addresses the practical steps that can be taken to make existing organizations (corporations, non-profits, government, etc.) Covers the most important aspects of human resource management and people analytics. Meets with 15.7611 when offered concurrently. We thank seminar and conference participants at Baruch College, Copenhagen Business School, UVA Darden, Federal Reserve Bank of Richmond, Federal Reserve Board, HEC Montreal, INSEAD, KAIST, Korea University, NYU Stern, the NYU Corporate Governance Lunch, Oxford University, SKK GSB, University Paris-Dauphine, Yonsei University, ABFER 2019 (Singapore), AFA 2018 (Philadelphia), CICF (Guangzhou) 2019, EFA 2019 (Carcavelos), NFA 2018 (Charlevoix), Korea Securities Association (KSA) Symposium (Seoul), CREDIT 2018 (Venice), Warsaw Conference in Finance 2018, IRMC 2017 (Florence), the Labex ReFi International Advisory Board Conference, and ESCP Paris for their insightful comments and suggestions. Employs a wide variety of learning tools, from experiential learning to the more conventional discussion of written cases. Exposes students to the major financial decisions made by leaders within a firm and to the ways the firm interacts with investors, with a focus on valuation. Students taking the graduate version complete additional assignments. This suggests that the increase in leverage is financing at least some incremental capital investment. No prior knowledge of law expected. Explores a basic marketing framework in depth as it applies to start-ups. Compute derivatives of Bessel functions of the first kind. No listeners. Includes a project in which student teams select and solve an optimization problem (possibly a large-scale problem) of practical interest. 2 Section 2 will provide more details about this discussion. Prereq: 15.501 U (Spring)3-0-6 unitsCredit cannot also be received for 15.518.
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