A consistent pricing process (CPP) is any representation of ( frictionless) "prices" of assets in a market. It is a stochastic process in a

filtered probability space Filtration is a physical separation process that separates solid matter and fluid from a mixture using a ''filter medium'' that has a complex structure through which only the fluid can pass. Solid particles that cannot pass through the filter ...

(\Omega,\mathcal,\_^T,P)

such that at time

t

the

i^

component can be thought of as a price for the

i^

asset. Mathematically, a CPP

Z = (Z_t)_^T

in a market with d-assets is an

adapted process In the study of stochastic processes, an adapted process (also referred to as a non-anticipating or non-anticipative process) is one that cannot "see into the future". An informal interpretation is that ''X'' is adapted if and only if, for every re ...

\mathbb^d

if ''Z'' is a martingale with respect to the physical probability measure

P

, and if

Z_t \in K_t^+ \backslash \

at all times

t

such that

K_t

is the

solvency cone The solvency cone is a concept used in financial mathematics which models the possible trades in the Market (economics), financial market. This is of particular interest to markets with transaction costs. Specifically, it is the convex cone of po ...

for the market at time

t

. The CPP plays the role of an equivalent martingale measure in markets with

transaction costs In economics and related disciplines, a transaction cost is a cost in making any economic trade when participating in a market. Oliver E. Williamson defines transaction costs as the costs of running an economic system of companies, and unlike pro ...

. In particular, there exists a 1-to-1 correspondence between the CPP

Z

and the EMM

Q

References

Financial risk modeling Mathematical finance {{econometrics-stub