
The authors consider a Black-Scholes type model of geometric Brownian motion with a jump at a random time, which appears in incomplete financial markets. They obtain a formula for the price of an Asian option at a random exponential maturity, so that the fixed maturity option price can be numerically computed by inverting the Laplace transform. The authors also consider a multi-jump case and derive an integro-differential equation whose solution leads to the time zero price of an Asian option.
Stochastic models in economics, Black-Scholes model, resolvent, Finance etc., Processes with independent increments; Lévy processes, incomplete financial market
Stochastic models in economics, Black-Scholes model, resolvent, Finance etc., Processes with independent increments; Lévy processes, incomplete financial market
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