Economic agents are exposed to the uncertain outcomes of future events. By enabling the exchange of securities, financial markets allow agents to reallocate their exposures in more efficient and mutually convenient arrangements to reduce perceived risks. The complexity and changing nature of the world in which agents operate make all markets incomplete, which means that there is scope for further risk reduction by the introduction of new market securities -- financial innovation -- to cover previously un-priced risks. This paper provides a convenient mathematical framework to solve the problem of dynamic equilibrium pricing and optimal design of new financial securities. Our mathematical tool for studying trading market equilibria is a novel theory of backward stochastic difference equations (BSÎEs) in discrete time, which we develop in analogy to the currently incomplete theory of backward stochastic differential equations (BSDEs) in continuous time. The new tool is used to define a ...
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