The paper introduces a simple way of recording and manipulating  stochastic processes without explicit reference to a probability measure. In the new calculus, operations traditionally presented in a measure-specific way are instead captured by tracing the behaviour of jumps (also when no jumps are physically present). The new calculus is thus intuitive and compact. The calculus is also fail-safe in that, under minimal assumptions, all formal calculations are guaranteed to yield mathematically well-defined stochastic processes. Several illustrative examples of the new concept are given , among them a novel result on the Margrabe option to exchange one defaultable asset for another.
The paper introduces a simple way of recording and manipulating general stochastic processes without explicit reference to a probability measure. In the new calculus, operations traditionally presented in a measure-specific way are instead captured by tracing the behaviour of jumps (also when no jumps are physically present). The calculus is fail-safe in that, under minimal assumptions, all informal calculations yield mathematically well-defined stochastic processes. The calculus is also intuitive as it allows the user to pretend all jumps are of compound Poisson type. The new calculus is very effective when it comes to computing drifts and expected values that possibly involve a change of measure. Such drift calculations yield, for example, partial integro-differential equations, Hamilton-Jacobi-Bellman equations, Feynman-Kac formulae, or exponential moments needed in numerous applications. We provide several illustrations of the new technique , among them a novel result on the Margrabe option to exchange one defaultable asset for another.
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general
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new calculus is thus intuitive and compact. The calculus is also
calculus is
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formal calculations are guaranteed to
informal calculations
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Several illustrative examples of the new concept are given
The calculus is also intuitive as it allows the user to pretend all jumps are of compound Poisson type. The new calculus is very effective when it comes to computing drifts and expected values that possibly involve a change of measure. Such drift calculations yield, for example, partial integro-differential equations, Hamilton-Jacobi-Bellman equations, Feynman-Kac formulae, or exponential moments needed in numerous applications. We provide several illustrations of the new technique