We study a bargaining scheme under which two agents update their beliefs
about the future states of the world in order to reach an agreement on the
price of a given contingent claim. We first formulate the problem as an
optimization problem and prove the existence of a solution for such problem
yielding a unique price for the contingent claim to be traded.
We introduce an extension to Merton's famous continuous time model of optimal
consumption and investment, in the spirit of previous works by Pliska and Ye,
to allow for a wage earner to have a random lifetime and to use a portion of
the income to purchase life insurance in order to provide for his estate, while
investing his savings in a financial market comprised of one risk-free security
and an arbitrary number of risky securities driven by multi-dimensional
Brownian motion.