static double Middle(int g, int r, double tau, double t)
{
double k = (tau < r) ? g : (tau < r+g) ? r+g-tau : 0;
Rk4 solver = new Rk4(
(double eta, double[] V, double[] res) =>
{ res[0] = -gp(tau) * h(eta, tau) * Inner(eta, k, t); },
1);
double[] reserves = solver.SolveFinal(120, 1, /* steps = */ 2, new double[] { 0.0 });
// Integral in state 0:
return reserves[0];
}
// GF820 computations. Notation as in Jeppe Woetmann Nielsen's note
// on 820 dated 2013-01-25. Female 35 year old insured life (method
// Outer), unknown male spouse (method Inner).
static double Inner(double eta, double k, double t)
{
Rk4 solver = new Rk4(
(double s, double[] V, double[] res) =>
{ res[0] = rate(t+s) * V[0] - indicator(s >= k) - GmMale(eta+s) * (0 - V[0]); },
1);
double[] reserves = solver.SolveFinal(120-eta, 0, steps, new double[] { 0.0 });
// Reserve in state 0:
return reserves[0];
}