how are the black scholes model the kelly criterion and the kalman filter related 
the black scholes model kelly criterion and the kalman filter are all mathematical systems that can be used to estimate investment returns when some key variables depend on unknown probabilities the black scholes model is used to calculate the theoretical value of options contracts based upon their time to maturity and other factors the kelly criterion is used to determine the optimal size of an investment based on the probability and expected size of a win or loss the kalman filter is used to estimate the value of unknown variables in a dynamic state where statistical noise and uncertainties make precise measurements impossible 