The system of PDEs with terminal conditions 2: singularity or stiff system suspected

Question

Constantly getting the following mistake:

NDSolve::ndsz: At t == 100.`, step size is effectively zero; singularity or stiff system suspected.

What could be done to resolve it?

V[t,z1,2] - is a time-dependent value function. The mistake should be solved in order to study its dynamics.

ClearAll["Global`*"]
tmax = 100; r = 1; lambda = 1; P = 100;

pdeV1 = D[V1[t, z1, z2], 
     t] + (1/2 + 1/2*z2^2)*(D[V1[t, z1, z2], z1])^2*Exp[r*t]*
     Exp[lambda*(z1 + z2)] + (1 + z1^2)*D[V1[t, z1, z2], z1]*
     D[V2[t, z1, z2], z1]*Exp[(r*t)]*
     Exp[(lambda*(z1 + z2))] + (D[V2[t, z1, z2], z2] + 
       D[V2[t, z1, z2], z2]*z1^2)*Exp[(r*t)]*(Exp[lambda*z1] - 1) == 0;


pdeV2 = D[V2[t, z1, z2], 
     t] + (1/2 + 1/2*z2^2)*(D[V2[t, z1, z2], z2])^2*Exp[(r*t)]*
     Exp[(lambda*(z1 + z2))] + (1 + z2^2)*D[V2[t, z1, z2], z2]*
     D[V1[t, z1, z2], z2]*Exp[(r*t)]*
     Exp[(lambda*(z1 + z2))] + (D[V1[t, z1, z2], z1] + 
       D[V1[t, z1, z2], z1]*z2^2)*
     Exp[(r*t)]*(Exp[(lambda*z2)] - 1) == 0;

sol = NDSolve[{pdeV1, pdeV2, 
   V1[tmax, z1, z2] == 
    P*Exp[(-lambda*z1)] - P*Exp[(-lambda*(z1 + z2))], 
   V2[tmax, z1, z2] == 
    P*Exp[(-lambda*z1)] - P*Exp[(-lambda*(z1 + z2))]}, {V1, V2}, {t, 
   0, tmax}, {z1, 0, 100}, {z2, 0, 100}, 
  Method -> {"MethodOfLines", 
    "SpatialDiscretization" -> {"TensorProductGrid", 
      "MinPoints" -> 5*15 + 1, "MaxPoints" -> 5*15 + 1, 
      "DifferenceOrder" -> Automatic}}]

Show[Plot3D[V1[tmax, z1, z2] /. sol, {z1, 0, 100}, {z2, 0, 100}, 
  PlotStyle -> Red], 
 Plot3D[V2[tmax, z1, z2] /. sol, {z1, 0, 100}, {z2, 0, 100}, 
  PlotStyle -> Purple]]