Paper on pricing and hedging in infinite-dimensional financial markets released
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Hanchao Liu released an academic paper extending the classical Black–Scholes market framework to infinite dimensions, modeling asset prices by stochastic evolution equations in a separable Hilbert space, deriving an infinite-dimensional Black–Scholes equation, and establishing exact-replication results for strong solutions and asymptotic-replication results for weak solutions. The study introduces a Hilbert-lattice structure to characterize no-arbitrage conditions, gives sufficient conditions for the existence and uniqueness of an equivalent risk-neutral measure, and provides explicit pricing formulas for partially tractable cases; the model can be interpreted as a segmented market composed of a family of one-dimensional geometric Brownian motions.
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- arXiv q-finPricing and Hedging Framework for Infinite-Dimensional Financial Markets
This study extends the classical Black-Scholes market framework to infinite-dimensional scenarios, modeling asset prices with stochastic evolution equations in separable Hilbert spaces, deriving an infinite-dimensional Black-Scholes equation, and establishing exact replication results for strong solutions and asymptotic replication results for weak solutions. The study also introduces Hilbert lattice structures to characterize no-arbitrage conditions, provides sufficient conditions for the existence and uniqueness of equivalent risk-neutral measures, and explicit pricing formulas for some tractable cases; the model can be interpreted as a segmented market composed of a series of one-dimensional geometric Brownian motions.
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