Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Nonlinear Filtering Revisited: A Spectral Approach
SIAM Journal on Control and Optimization
Approximation of the Kushner Equation for Nonlinear Filtering
SIAM Journal on Control and Optimization
Time Series Analysis and Its Applications (Springer Texts in Statistics)
Time Series Analysis and Its Applications (Springer Texts in Statistics)
Information theory and statistics: a tutorial
Communications and Information Theory
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Merton's model views equity as a call option on the asset of the firm. Thus the asset is partially observed through the equity. Then using nonlinear filtering an explicit expression for likelihood ratio for underlying parameters in terms of the nonlinear filter is obtained. As the evolution of the filter itself depends on the parameters in question, this does not permit direct maximum likelihood estimation, but does pave the way for the 'Expectation-Maximization' method for estimating parameters.