Consider the geometric Poisson model with the price evolution dXY (t) = (e ? - 1)XY (t-)d(N(t) - ? Y

Consider the
geometric Poisson model with the price evolution

dXY (t) = (e
γ − 1)XY (t−)d(N(t) − λ Y t). (a) Find the price of
a contract that pays off a unit of an asset X when N(T ) = k. (b) Find the
price of a contract that pays off a unit of an asset Y when N(T ) = k. (c)
Which of the two contracts is more valuable? Find a condition for k for which
the contract that pays off the asset X is more valuable (inequality in terms of
γ, λY , T, and XY (0)).