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Explore types of clauses and CNFs for derivative trading. Determine price for derivatives using polynomial time algorithms. Unique pricing mechanism with profit/loss scenarios.
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Types for CNFs • Type of a clause: • Pair: (length, positive literals) • Example: (2,2) for (a or b) • Type of a cnf: • Set union of types of clauses • Example: T = ((2,2) (1,0)) for (a or b) and (b or c) and !a and !b and !c
CNF type as derivative • Determine price p in [0,1] for derivative T, e.g., price for ((2,2) (1,0)). • When I buy your derivative T at a price p you have the obligation to give me a cnf of type T and the fraction of the clauses that I can satisfy you have to pay me. What is your price for derivative T?
Fact • There is a unique price p(T) for derivative T: • p > p(T) you make money • p <p(T) you lose money • Assumes that I have only polynomial time available, e.g., quadratic polynomial time.
