Most recently I read Isaac Asimov's science fiction novels and know about his famous "Three Laws of Robotics" (https://en.wikipedia.org/wiki/Three_Laws_of_Robotics). But I am not so convinced by his first rule "A robot may not injure a human being", especially when AI reaches status of Artificial General intelligence (AGI) or even Artificial Super intelligence (ASI). What if in the near future, among a group of AIs, some of them follow this no-harm rule but the rest don't? I am curious about what's the probability these AIs reach a consensus to start harming people? I would like to build some mathmetical/probability/simulation models to best fit the scenario and calculate the probability. Any thoughts or discussion will be very welcome.

In this blog, we will summarize the latex code of most popular formulas and equations for Financial Engineering Formula and Equation (Continuous-Time Finance). We will cover important topics including Standard Brownian Motion (SBM), Geometric Brownian Motion (GBM), Ito Lemma, Stochastic Integrals, Solutions to Some Common SDEs, Brownian Motion Variation, Stock Prices as a GBM, Stock Prices are Lognormal, Sharpe Ratio and Hedging, The Black-Scholes Equation, Risk-Neutral Valuation and Power Contracts.

In this blog, we will summarize the latex code for differential equations formulas, including diffusion (conduction) equation, wave equation, heat equation, laplace equation, Legendre's equation, Bessel's equation, Spherical Harmonics Equation, etc.

In this blog, we will summarize the latex code of most popular formulas and equations for Financial Engineering Formula and Equation (Continuous-Time Finance). We will cover important topics including Standard Brownian Motion (SBM), Geometric Brownian Motion (GBM), Ito Lemma, Stochastic Integrals, Solutions to Some Common SDEs, Brownian Motion Variation, Stock Prices as a GBM, Stock Prices are Lognormal, Sharpe Ratio and Hedging, The Black-Scholes Equation, Risk-Neutral Valuation and Power Contracts.

In this blog, we will summarize the latex code for basic calculus formulas, including Limits, Differentiation and Integration. For integration formulas, we will cover the topic as standard form of integration, integration of 1/x, ln(x), Exponential e^{ax}, xe^{ax}, Integration by Parts, Differentiation of an Integral, Dirac Delta Function, etc.

In this blog, we will summarize the latex code for series formulas, including arithmetic and geometric progressions, convergence of series: the ratio test, Binomial expansion, Taylor and Maclaurin Series, Power Series with Real Variables e^{x},ln(1+x),sin(x),cos(x), Plane Wave Expansion, etc.

In this blog, we will summarize the latex code for linear matrix algebra formulas, including matrix multiplication, transpose, inverse matrix, determinants, hermitian matrices, determinants, eigenvalues and eigenvectors, orthogonal matrices, etc.

In this blog, we will summarize the latex code for basic calculus formulas, including Limits, Differentiation and Integration. For limits formulas, we will cover sections including: L'Hospital Rule, Limits of Power, Limits of xln(x), Limits of x^{n}/n!. For differentiation formulas, we will cover Differentiation of Polynomial Function, Chain Rule for Differentiation, Differentiation of Multiplication, Differentiation of Division, Differentiation of Trigonometric formulas (sin, cos, tan, sec), and Differentiation of Hyperbolic formulas (sinh, cosh, tanh, sech, coth, cosech).

In this blog, we will summarize the latex code for Curves and Shapes, Geometry Math Formulas. Topics include Distance Between Two Points 2D, Distance Between Two Points 3D, Eccentricity of a Hyperbola, Eccentricity of an Ellipse, Circle, Hyperbola, Hyperbolic Paraboloid, Parabola, Plane, Sphere, Ellipse, Ellipsoid, Elliptic Cone, Elliptic Cylinder, Elliptic Paraboloid, Spiral of Archimedes, etc.

In this blog, we will summarize the latex code of most popular formulas and equations for Financial Engineering Formula and Equation part I-Forwards, Puts, and Calls. We will cover important topics including Forwards, Put-Call Parity, Calls and Puts with Different Strikes, Calls and Puts Arbitrage, Call and Put Price Bounds, Varying Times to Expiration, Early Exercise for American Options, etc.

In this blog, we will summarize the latex code for Geometry, Math formulas and equations. Topics include Area of a Circle, Area of a Parallelogram, Area of a Rectangle, Area of a regular Polygon, Area of a Rhombus, Area of a Sector, Area of a Square, Area of a Trapezoid, Area of a Triangle,Area of an Ellipse, Area of an Equilateral Triangle.

Most recently I read Isaac Asimov's science fiction novels and know about his famous "Three Laws of Robotics" (https://en.wikipedia.org/wiki/Three_Laws_of_Robotics). But I am not so convinced by his first rule "A robot may not injure a human being", especially when AI reaches status of Artificial General intelligence (AGI) or even Artificial Super intelligence (ASI). What if in the near future, among a group of AIs, some of them follow this no-harm rule but the rest don't? I am curious about what's the probability these AIs reach a consensus to start harming people? I would like to build some mathmetical/probability/simulation models to best fit the scenario and calculate the probability. Any thoughts or discussion will be very welcome.

In this blog, we will summarize the latex code for Geometry Coordinate Systems, Math Formulas. Topics include Cartesian to Cylindrical Coordinates, Cartesian to Polar Coordinates, Cartesian to Spherical Coordinates, Cylindrical to Spherical Coordinates, etc.

In this blog, we will summarize the latex code of most popular formulas and equations for Financial Engineering Formula and Equation Monte-Carlo Simulations and Interest Rate Models. We will cover important topics including Monte-Carlo Simulations, Bonds and Interest Rates, Black-Derman-Toy (BDT) model and Cox-Ingersoll-Ross (CIR) model.

In this blog, we will summarize the latex code of most popular formulas and equations for Financial Engineering Formula and Equation (Continuous-Time Finance). We will cover important topics including Standard Brownian Motion (SBM), Geometric Brownian Motion (GBM), Ito Lemma, Stochastic Integrals, Solutions to Some Common SDEs, Brownian Motion Variation, Stock Prices as a GBM, Stock Prices are Lognormal, Sharpe Ratio and Hedging, The Black-Scholes Equation, Risk-Neutral Valuation and Power Contracts.

In this blog, we will summarize the latex code of most popular formulas and equations for Financial Engineering Formula and Equation (Continuous-Time Finance). We will cover important topics including Standard Brownian Motion (SBM), Geometric Brownian Motion (GBM), Ito Lemma, Stochastic Integrals, Solutions to Some Common SDEs, Brownian Motion Variation, Stock Prices as a GBM, Stock Prices are Lognormal, Sharpe Ratio and Hedging, The Black-Scholes Equation, Risk-Neutral Valuation and Power Contracts.

In this blog, we will summarize the latex code of most popular formulas and equations for Financial Engineering Formula and Equation part I-Forwards, Puts, and Calls. We will cover important topics including Forwards, Put-Call Parity, Calls and Puts with Different Strikes, Calls and Puts Arbitrage, Call and Put Price Bounds, Varying Times to Expiration, Early Exercise for American Options, etc.

In this blog, we will summarize the latex code of most popular formulas and equations for Financial Engineering Formula and Equation Monte-Carlo Simulations and Interest Rate Models. We will cover important topics including Monte-Carlo Simulations, Bonds and Interest Rates, Black-Derman-Toy (BDT) model and Cox-Ingersoll-Ross (CIR) model.