Math Problem Statement
\begin{align} \frac{\partial q(V, \tau)}{\partial \tau} &= (\mu_{V} - \lambda_{V}) \frac{\partial q(V, \tau)}{\partial V} + \frac{1}{2} \sigma_{V}^2 V^2 \frac{\partial^2 q(V, \tau)}{\partial V^2} \nonumber \end{align} with boundary condition $q(V, 0) = 1 /V.$
solve PDE
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Partial Differential Equations (PDEs)
Linear Parabolic Equations
Cox-Ingersoll-Ross (CIR) Model
Formulas
PDE form: \( \frac{\partial q(V, \tau)}{\partial \tau} = (\mu_{V} - \lambda_{V}) \frac{\partial q(V, \tau)}{\partial V} + \frac{1}{2} \sigma_{V}^2 V^2 \frac{\partial^2 q(V, \tau)}{\partial V^2} \)
Theorems
-
Suitable Grade Level
Advanced
Related Recommendation
Functional Form for Q with Parameters μV, λV, σV
Solving Nonlinear Differential Equations with Power-Law Terms for Equilibrium
Solve Heat Equation in Cylindrical Coordinates with Laser Pulse and Heat Losses
Compute y(0.12) Using Taylor’s Series Method
Solving the Second-Order PDE x²r - 2xs + t + q = 0 Using Monge's Method