Minimal martingale measure: Pricing and hedging in a pure jump model under restricted information

Abstract

Financial asset price movements are considered in a model with partial information. The risky assets’ price is modeled as a marked point process. The underlying event arrival process, which is again a marked point process, is assumed to be unobserved by the market agents. Taking into account the presence of catastrophic events, the possibility of common jump times between the risky assets’ price process and the arrival process is allowed. The problem of characterizing the equivalent martingale measures is investigated and in particular the minimal martingale measure is studied. The hedging and the pricing problem of a European contingent claim are discussed. The arbitrage-free price is identified with the conditional expectation with respect to the observations under the minimal martingale measure.