Risk evaluation

Risk evaluation

1. On policy level:

   • n incidents during a certain time period
     • Total loss z = x_1+...+x_n,
       • where x_i denotes the loss of the i-th incident

2. On portfolio level:

   • N different claim sizes during a certain time period
     • Total portfolio loss Z = X_1+...+X_N,
       • where X_i denotes the total loss of the i-th type of claim

3. Compensations will differ according to the type of contract:

   • z = actual total replacement value, f(x)= actual compensation of the each loss:
     • z = f(x_1)+...+f(x_n)
     • Given the i-th loss x_i, the contract f(x_i) determines the i-th compensation.
       • Can now include the possibility of e.g. only covering losses x_i within a certain range, say [y,y+b], for y,b > 0:
         • f(x_i) = 0 if x_i < y
           • f(x_i) = x_i - y, if y < x_i < y+b
             • f(x_i) = b, if x_i > y+b
               • where y denotes a certain deductible
                 • (Reinsurance can be arranged in a similar way)
   • The insurance company is not necessarily obliged to cover the whole loss of the policy holder!