One Reserve Question, please

[yarawa]

Given a 3-year term insurance bought by (50) defined as follows: Let b(k+1) be the death benefit to be paid at time k+1 if (50) dies within the (k+1)st year: b1=1,b2=2 and b3=2.

Given: 0/q50=.005, 1/q50=.006, 2/q50=.oo7 and v=.8.
With P determined so that u(w) =E{u(w-L)} where u(w)=-e^(-0.1w). We can found P=.008. Use the same utility of wealth function to determine 1V(the exponential reserve) for this value of P.

From Temple University Manual, p133

[Jim Daniel]

Just solve for V in the equation
e^(0.1 V) = E[e^(0.1 L)] where L is the present-value-of-future-loss random variable after 1 year. Note that L can only take on 3 different values.

Jim Daniel