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Maybe a quant researcher, but first of all I think I gotta get the phd. I would apply for a phd in computational mathematics / applied mathematics / probability. I'd pursue the phd not only to be a quant, i'm really interested in the reseach/academia experience.
Do you think I'm able to work in quant finance just by looking at my background?
Do you think i need a MSc in Quant Finance so as to reinforce my financial knowledge? is my background good enough?
What kind of quant do you think i could be?
Software: Excel (No VBA), Python, R, SQL, Easy Matlab (i'm thinking about learning C++)
Jobs: Health/Life Actuary and Professor
PROBABILITY
Random vectors. Probability and joint density function. Independence. Sums of random variables. Conditional hope. Multivariate normal distribution, Law of Large Numbers, Central Limit Theorem and Multivariate Central Limit Theorem. Multivariate Delta Method.
INTRODUCTION TO STATISTICAL LEARNING
Exploratory data methods. Summary measures. Boxplot. Relative frequency. Histograms. Density estimation. Naive Bayes Classification. Regression Models. Estimation of the regression function. Non-parametric estimators: Nadaraya, KNN. Clusters by the k-means method
ESTIMATION METHODS
Estimate. Bias, variance and mean square error. Bias-variance compromise. Estimation in parametric models: maximum likelihood, moments, M estimators. Asymptotic properties: consistency and asymptotic distribution. Confidence intervals for the mean of a normal distribution with known variance. Confidence intervals for the mean of a normal distribution with unknown variance: Student's t distribution. Asymptotic level confidence intervals based on asymptotically normal statistics. Confidence intervals for proportions. Confidence intervals for two samples. Bootstrap.
STATISTICAL INFERENCE
Null and alternative hypotheses. Types of errors. Level and power of a test. "p" value. Tests for the mean of a normal population with known variance and with unknown variance. Wald tests (based on asymptotically normal statistics). Tests and confidence intervals for two samples. Relationship between tests and confidence intervals. Comparison of the vector of means of two multivariate populations. The problem of multiple comparisons or simultaneous coverage. Non-parametric tests.
LINEAR MODEL
Population linear optimum. Least Squares. Assumptions. Inference for model parameters: under normality and asymptotic theory. Prediction. Nonlinear regression. Fit and overfit. Regularization methods (Ridge, Lasso, etc.). Model-method evaluation techniques and metrics (cross-validation, etc.)
DATA REDUCTION AND VISUALIZATION TECHNIQUES
Cluster,T-sne. Classification. ROC curves. Dimension reduction: principal components, canonical correlation, projection pursuit.
SUPERVISED LEARNING
Decision trees. Logistic regression: parameter estimation by maximum likelihood. Neural Networks. Generalized linear model. Model-method evaluation techniques and metrics (cross-validation, etc.)
TIME SERIES
Identification of atypical observations and level changes. Transfer function. Vector autoregressive models. Vector ARIMA models. Kalman filters. Softeners. Conditionally heteroscedastic models. ARCH and GARCH models.
MULTIVARIATE ANALYSIS TECHNIQUES
Wishart Distribution. Distribution of maximum likelihood estimators. Hotelling Distribution. Hotelling test. Application to the two-sample problem and analysis of variance. Rao's U statistician. Applications of the Hotelling test. Fisher-Behrens problem. Profile analysis. Multivariate linear model. Multivariate analysis of variance. Multidimensional scaling. Correspondence analysis. Factorial analysis. Curves and main surfaces. Sufficient reduction
COMPUTATIONAL STATISTICS
Computation of Maximum Likelihood and M-type estimators. The EM algorithm. Fundamentals and Applications. Monte Carlo methods based on Markov chains. Parametric and non-parametric Bootstrap. Robust Boostrap.
ORDINARY DIFFERENTIAL EQUATIONS
1.1st differential equations. Order and models: Introduction to modeling and systems. Separable differential equations. Planar systems and first-order ordinary differential equations. Systems of first order differential equations. 2. Fundamental theory: Existence of solutions. Extension of solutions. Uniqueness of solutions. Continuity of solutions with respect to parameters. Differentiability with respect to parameters. 3. Linear systems: Homogeneous and inhomogeneous linear systems. Linear systems with constant coefficients. Asymptotic behavior of solutions of linear systems with constant coefficients. Linear systems with periodic coefficients. 4. Stability: The concept of equilibrium point. Definitions of stability and bounding. Linear systems. Second order linear systems. Phase plan. Lyapunov functions. Lyapunov stability and instability theorems. Invariance theory. Domains of attraction. Inverse theorems. 5. Disturbance of linear systems: Stability of an equilibrium point. The stable variety. Asymptotic equivalence.
PDEs AND APPLICATIONS.
1.Classification of partial differential equations. 2. Models that involve different types of equations. Classic examples of elliptic, parabolic and hyperbolic equations. 3. Results on existence, uniqueness and regularity of solutions. 4. Numerical methods: Finite differences and Galerkin approximations. Computational implementation of the methods in simple cases.
MEASURE THEORY AND INTEGRATION.
1.Measurements on sigma-algebras of sets, probability measures. 2. Integration with respect to a measure, limit passage theorems. 3. Product measure, Fubini's theorem. 4. Radon-Nikodym theorem, conditional expectations. 5. Lebesgue measure, Lebesgue integral, relationship between integration and differentiation. 6. Convolution, identity approximations. 7. Spaces L p .
FINANCIAL MATHEMATICS
1.Markets, products and derivatives. Time value of money. Interest rates and present value. Basic assets. Derivative instruments. Types of options. Value of an option. "Payoff" and profit strategies and diagrams. Put-call parity. Hedging and Arbitration. Options modeling. 2. Elements of Statistics. Results on set theory. Probabilistic definitions. Stochastic processes. Representation of the flow of information. Conditional expectation. Distribution and probability density functions. moments. Relevant distributions in finance. 3. Random nature of the market. Discrete returns model. Random walk. Martingales. Brownian movement. Ito Integral. Functions of a random variable. Ito motto. Stochastic differential equations. Continuous returns model. 4. Partial differential equations - Black-Scholes equation. The diffusion equation. Initial and boundary conditions. Reduction for similarity. Explicit solutions of the diffusion equation. Black-Scholes hypothesis. The Black-Scholes equation. Boundary and end conditions. Solution for European options: Black-Scholes formulas. Black-Scholes extensions. Sensibilities of a portfolio: the “Greeks”. Implied volatility. American options. Free border problems. 5. Exotic and path-dependent options. Barrier options. Differential equations for strongly path-dependent options. Lookback and Asian options. Jump conditions for discrete sampling. Reduction for similarity. 6. Martingales in continuous tense. Doob-Meyer decomposition. Exponential Martingales. Equivalent probability measures. Girsanov's theorem. 7. Continuous time finance- Arbitrage Pricing Theory (APT). Basic model of the economy. Self-financed strategies. Arbitrage strategies. Evaluation of derivatives prices from the point of view of the APT. Equivalence between Black-Scholes treatment and APT. Kolmogorov equations.
INTRODUCTION TO MATHEMATICAL CONTROL THEORY
Part I: Classical control theory. 1. Controllability and Observability: Controllability Matrix. Range condition. Kalman decomposition. Observability. 2. Stability and stabilization: Stable linear systems. Stable polynomials. Stability, observability and the Lyapunov equation. Stability and controllability. Detectability and dynamic observers. 3. Realization theory: Impulsive response and transfer functions. Realizations of the function of the impulsive response. Part II: Nonlinear control system. 4. Controllability and Observability of nonlinear systems: Controllability and linearization. Lie brackets. The character of the reachability set. Observability. 5. Stability and stabilization: Lyapunov's indirect method. The method of Lyapunov functions. LaSalle's theorem. Exponential stability and robustness. Necessary conditions for stabilization. 6. Theory of realization: Input-output functions. Partial realizations. Part III: Optimal control. 7. Dynamic programming: The Bellman equation and the value function. The quadratic regulator problem. The Riccatti equation. The quadratic regulator and stabilization. 8. The maximum principle: Control problems with fixed final time. The maximum principle for impulsive control problems. Optimal timing problems.
VARIATIONAL CALCULUS
1.Introduction: Functional. Simple variational problems. Functional spaces. The variation of a functional. Necessary condition for the existence of an extreme. The simplest variational problem. Euler equations. The multivariable case. A simple problem with moving boundary point. Invariance of Euler's equation. 2. Generalizations: The problem with fixed boundary point for n unknown functions. 3. Variational problems in parametric form. Functionals that depend on higher order derivatives. Variational problems with additional conditions. 4. The general variation of a functional: Obtaining the basic formula. The case of boundary points that lie on two curves or surfaces. Soft chunky ends. The Weierstrass-Erdmann conditions. 5. Canonical form of Euler's equations: The canonical form of Euler's equations. First integrals of Euler's equations. Legendre's transformation. 6. canonical transformations. Noether's theorem. The principle of least action. Conservation laws. Hamilton-Jacobi equation. 7. The second variation. Sufficient conditions for the existence of a weak extreme: Quadratic functionals. The second variation of a functional one. Formula for the second variation. Legendre condition. Jacobi necessary condition. 8. Sufficient conditions for the existence of a weak end. Generalization to the case of n unknown functions. 9. Fields. Sufficient conditions for the existence of a strong end: Consistent boundary conditions. Fields. The field of a functional. 10. Hilbert invariant integral. Weierstrass condition E. Sufficient conditions for the existence of a strong extreme.
ADVANCED NUMERICAL ANALYSIS
1.Partial differential equations: Type equations. Classification. The characteristic curves. 2. Introduction to the method of finite differences: Parabolic problems. Hyperbolic problems. Elliptical problems. 3. Introduction to the finite element method: Weighted residual method. Weak formulation. Bubnov-Galerkin method. Petrov-Galerkin method. Variational formulation. Evolutionary problems. 4. Introduction to the method of finite volumes: Scheme of the cell vertex. Scheme centered on the cell. 5. Introduction to the method of boundary elements: Direct integral formulation. Green's Function Method. Indirect integral formulation. Image method. Panel method.
FOURIER ANALYSIS
1. Fourier series, Fourier transformations, convolutions, Plancherel theorems. 2. Discrete Fourier transform, applications, fast Fourier transform. 3. Distributions, Fourier transform of distributions, convergence of distributions. 4. Sampling, interpolation, reconstruction of functions from their samples. 5. Partial differential equations: wave equation, diffusion equation, diffraction equation. 6. Wavelets, Haar wavelets, compactly supported wavelets, analysis and synthesis with Daubechies wavelets, filter banks.
Do you think I'm able to work in quant finance just by looking at my background?
Do you think i need a MSc in Quant Finance so as to reinforce my financial knowledge? is my background good enough?
What kind of quant do you think i could be?
Software: Excel (No VBA), Python, R, SQL, Easy Matlab (i'm thinking about learning C++)
Jobs: Health/Life Actuary and Professor
Background:
Bachelor degree (Argentina): Economics
Certification (USA): ASA (Society of Actuaries)
Bachelor degree (Argentina): Economics
Certification (USA): ASA (Society of Actuaries)
Master degree (Argentina): Statistics:
PROBABILITY
Random vectors. Probability and joint density function. Independence. Sums of random variables. Conditional hope. Multivariate normal distribution, Law of Large Numbers, Central Limit Theorem and Multivariate Central Limit Theorem. Multivariate Delta Method.
INTRODUCTION TO STATISTICAL LEARNING
Exploratory data methods. Summary measures. Boxplot. Relative frequency. Histograms. Density estimation. Naive Bayes Classification. Regression Models. Estimation of the regression function. Non-parametric estimators: Nadaraya, KNN. Clusters by the k-means method
ESTIMATION METHODS
Estimate. Bias, variance and mean square error. Bias-variance compromise. Estimation in parametric models: maximum likelihood, moments, M estimators. Asymptotic properties: consistency and asymptotic distribution. Confidence intervals for the mean of a normal distribution with known variance. Confidence intervals for the mean of a normal distribution with unknown variance: Student's t distribution. Asymptotic level confidence intervals based on asymptotically normal statistics. Confidence intervals for proportions. Confidence intervals for two samples. Bootstrap.
STATISTICAL INFERENCE
Null and alternative hypotheses. Types of errors. Level and power of a test. "p" value. Tests for the mean of a normal population with known variance and with unknown variance. Wald tests (based on asymptotically normal statistics). Tests and confidence intervals for two samples. Relationship between tests and confidence intervals. Comparison of the vector of means of two multivariate populations. The problem of multiple comparisons or simultaneous coverage. Non-parametric tests.
LINEAR MODEL
Population linear optimum. Least Squares. Assumptions. Inference for model parameters: under normality and asymptotic theory. Prediction. Nonlinear regression. Fit and overfit. Regularization methods (Ridge, Lasso, etc.). Model-method evaluation techniques and metrics (cross-validation, etc.)
DATA REDUCTION AND VISUALIZATION TECHNIQUES
Cluster,T-sne. Classification. ROC curves. Dimension reduction: principal components, canonical correlation, projection pursuit.
SUPERVISED LEARNING
Decision trees. Logistic regression: parameter estimation by maximum likelihood. Neural Networks. Generalized linear model. Model-method evaluation techniques and metrics (cross-validation, etc.)
TIME SERIES
Identification of atypical observations and level changes. Transfer function. Vector autoregressive models. Vector ARIMA models. Kalman filters. Softeners. Conditionally heteroscedastic models. ARCH and GARCH models.
MULTIVARIATE ANALYSIS TECHNIQUES
Wishart Distribution. Distribution of maximum likelihood estimators. Hotelling Distribution. Hotelling test. Application to the two-sample problem and analysis of variance. Rao's U statistician. Applications of the Hotelling test. Fisher-Behrens problem. Profile analysis. Multivariate linear model. Multivariate analysis of variance. Multidimensional scaling. Correspondence analysis. Factorial analysis. Curves and main surfaces. Sufficient reduction
COMPUTATIONAL STATISTICS
Computation of Maximum Likelihood and M-type estimators. The EM algorithm. Fundamentals and Applications. Monte Carlo methods based on Markov chains. Parametric and non-parametric Bootstrap. Robust Boostrap.
Master degree (Argentina): Engineering Mathematics
ORDINARY DIFFERENTIAL EQUATIONS
1.1st differential equations. Order and models: Introduction to modeling and systems. Separable differential equations. Planar systems and first-order ordinary differential equations. Systems of first order differential equations. 2. Fundamental theory: Existence of solutions. Extension of solutions. Uniqueness of solutions. Continuity of solutions with respect to parameters. Differentiability with respect to parameters. 3. Linear systems: Homogeneous and inhomogeneous linear systems. Linear systems with constant coefficients. Asymptotic behavior of solutions of linear systems with constant coefficients. Linear systems with periodic coefficients. 4. Stability: The concept of equilibrium point. Definitions of stability and bounding. Linear systems. Second order linear systems. Phase plan. Lyapunov functions. Lyapunov stability and instability theorems. Invariance theory. Domains of attraction. Inverse theorems. 5. Disturbance of linear systems: Stability of an equilibrium point. The stable variety. Asymptotic equivalence.
PDEs AND APPLICATIONS.
1.Classification of partial differential equations. 2. Models that involve different types of equations. Classic examples of elliptic, parabolic and hyperbolic equations. 3. Results on existence, uniqueness and regularity of solutions. 4. Numerical methods: Finite differences and Galerkin approximations. Computational implementation of the methods in simple cases.
MEASURE THEORY AND INTEGRATION.
1.Measurements on sigma-algebras of sets, probability measures. 2. Integration with respect to a measure, limit passage theorems. 3. Product measure, Fubini's theorem. 4. Radon-Nikodym theorem, conditional expectations. 5. Lebesgue measure, Lebesgue integral, relationship between integration and differentiation. 6. Convolution, identity approximations. 7. Spaces L p .
FINANCIAL MATHEMATICS
1.Markets, products and derivatives. Time value of money. Interest rates and present value. Basic assets. Derivative instruments. Types of options. Value of an option. "Payoff" and profit strategies and diagrams. Put-call parity. Hedging and Arbitration. Options modeling. 2. Elements of Statistics. Results on set theory. Probabilistic definitions. Stochastic processes. Representation of the flow of information. Conditional expectation. Distribution and probability density functions. moments. Relevant distributions in finance. 3. Random nature of the market. Discrete returns model. Random walk. Martingales. Brownian movement. Ito Integral. Functions of a random variable. Ito motto. Stochastic differential equations. Continuous returns model. 4. Partial differential equations - Black-Scholes equation. The diffusion equation. Initial and boundary conditions. Reduction for similarity. Explicit solutions of the diffusion equation. Black-Scholes hypothesis. The Black-Scholes equation. Boundary and end conditions. Solution for European options: Black-Scholes formulas. Black-Scholes extensions. Sensibilities of a portfolio: the “Greeks”. Implied volatility. American options. Free border problems. 5. Exotic and path-dependent options. Barrier options. Differential equations for strongly path-dependent options. Lookback and Asian options. Jump conditions for discrete sampling. Reduction for similarity. 6. Martingales in continuous tense. Doob-Meyer decomposition. Exponential Martingales. Equivalent probability measures. Girsanov's theorem. 7. Continuous time finance- Arbitrage Pricing Theory (APT). Basic model of the economy. Self-financed strategies. Arbitrage strategies. Evaluation of derivatives prices from the point of view of the APT. Equivalence between Black-Scholes treatment and APT. Kolmogorov equations.
INTRODUCTION TO MATHEMATICAL CONTROL THEORY
Part I: Classical control theory. 1. Controllability and Observability: Controllability Matrix. Range condition. Kalman decomposition. Observability. 2. Stability and stabilization: Stable linear systems. Stable polynomials. Stability, observability and the Lyapunov equation. Stability and controllability. Detectability and dynamic observers. 3. Realization theory: Impulsive response and transfer functions. Realizations of the function of the impulsive response. Part II: Nonlinear control system. 4. Controllability and Observability of nonlinear systems: Controllability and linearization. Lie brackets. The character of the reachability set. Observability. 5. Stability and stabilization: Lyapunov's indirect method. The method of Lyapunov functions. LaSalle's theorem. Exponential stability and robustness. Necessary conditions for stabilization. 6. Theory of realization: Input-output functions. Partial realizations. Part III: Optimal control. 7. Dynamic programming: The Bellman equation and the value function. The quadratic regulator problem. The Riccatti equation. The quadratic regulator and stabilization. 8. The maximum principle: Control problems with fixed final time. The maximum principle for impulsive control problems. Optimal timing problems.
VARIATIONAL CALCULUS
1.Introduction: Functional. Simple variational problems. Functional spaces. The variation of a functional. Necessary condition for the existence of an extreme. The simplest variational problem. Euler equations. The multivariable case. A simple problem with moving boundary point. Invariance of Euler's equation. 2. Generalizations: The problem with fixed boundary point for n unknown functions. 3. Variational problems in parametric form. Functionals that depend on higher order derivatives. Variational problems with additional conditions. 4. The general variation of a functional: Obtaining the basic formula. The case of boundary points that lie on two curves or surfaces. Soft chunky ends. The Weierstrass-Erdmann conditions. 5. Canonical form of Euler's equations: The canonical form of Euler's equations. First integrals of Euler's equations. Legendre's transformation. 6. canonical transformations. Noether's theorem. The principle of least action. Conservation laws. Hamilton-Jacobi equation. 7. The second variation. Sufficient conditions for the existence of a weak extreme: Quadratic functionals. The second variation of a functional one. Formula for the second variation. Legendre condition. Jacobi necessary condition. 8. Sufficient conditions for the existence of a weak end. Generalization to the case of n unknown functions. 9. Fields. Sufficient conditions for the existence of a strong end: Consistent boundary conditions. Fields. The field of a functional. 10. Hilbert invariant integral. Weierstrass condition E. Sufficient conditions for the existence of a strong extreme.
ADVANCED NUMERICAL ANALYSIS
1.Partial differential equations: Type equations. Classification. The characteristic curves. 2. Introduction to the method of finite differences: Parabolic problems. Hyperbolic problems. Elliptical problems. 3. Introduction to the finite element method: Weighted residual method. Weak formulation. Bubnov-Galerkin method. Petrov-Galerkin method. Variational formulation. Evolutionary problems. 4. Introduction to the method of finite volumes: Scheme of the cell vertex. Scheme centered on the cell. 5. Introduction to the method of boundary elements: Direct integral formulation. Green's Function Method. Indirect integral formulation. Image method. Panel method.
FOURIER ANALYSIS
1. Fourier series, Fourier transformations, convolutions, Plancherel theorems. 2. Discrete Fourier transform, applications, fast Fourier transform. 3. Distributions, Fourier transform of distributions, convergence of distributions. 4. Sampling, interpolation, reconstruction of functions from their samples. 5. Partial differential equations: wave equation, diffusion equation, diffraction equation. 6. Wavelets, Haar wavelets, compactly supported wavelets, analysis and synthesis with Daubechies wavelets, filter banks.
