Abstract:
This paper considers a class of incomplete financial market
models with security price processes that exhibit intensity based jumps.
The benchmark or numeraire is chosen to be the growth optimal
portfolio. Portfolio values, when expressed in units of the benchmark,
are local martingales. In general, an equivalent risk neutral martingale
measure need not exist in the proposed framework. Benchmarked
fair derivative prices are defined as conditional expectations of future
benchmarked prices under the real world probability measure. This
concept of fair pricing generalizes classical risk neutral pricing. The
pricing under incompleteness is modeled by the choice of the market
prices for risk. The hedging is performed under minimization of profit
and loss fluctuations.
