# -*- coding: utf-8 -*-

"""

Created on Mon Nov 7 16:35:02 2016

@author: d_floriello

Example Risk calculation

"""

import numpy as np

import sdeint

import matplotlib.pyplot as plt

from sympy.solvers.pde import pdsolve

from sympy import Function, diff, Eq, cos, sin

from sympy.abc import x, t

# Weiner Process Simulation

f = Function('f')

u = f(x, t)

ux = u.diff(x)

ut = u.diff(t)

uxx = ux.diff(x)

eq = Eq(ut + (1 - cos(2*x)*u + (x + 2 - sin(2*x))*ux - 0.5*(sin(x)**2)*uxx))

pdsolve(eq)

# Time steps

n = 1000

T = 1

###############################################################################

def Wiener(mu, sig, n, T):

return S

###############################################################################

plt.figure()

plt.plot(Wiener(0,1,n,T))

def mu(x,t):

return x**2

def SIG(x, t):

return np.sqrt(x)

tspan = np.linspace(0.0, 1, 10001)

res = sdeint.itoint(mu, SIG, 1, tspan)

plt.figure()

plt.plot(tspan,res.ravel())

def mu2(x,t):

return x + 2

def sig2(x,t):

return np.sin(x)

plt.figure()

tspan2 = np.linspace(0.0, 1, 10001)

for i in range(10):

plt.plot(tspan2, sdeint.itoint(mu2, sig2, 0, tspan2))

def ForwardKolmogorovEquation(drift, diffusion):

return pdsolve(eq)

drift = Function('x + 2')

diffusion = Function('sin(x)')

ForwardKolmogorovEquation(drift, diffusion)