Pointwise Arbitrage Pricing Theory in Discrete Time
Copyright policy )Pointwise Arbitrage Pricing Theory in Discrete Time
We develop a robust framework for pricing and hedging of derivative securities in discrete-time financial markets. We consider markets with both dynamically and statically traded assets and make minimal measurability assumptions. We obtain abstract (pointwise) fundamental theorem of asset pricing and pricing–hedging duality. Our results are general and, in particular, cover both the so-called model independent case as well as the classical probabilistic case of Dalang–Morton–Willinger. Our analysis is scenario-based: a model specification is equivalent to a choice of scenarios to be considered. The choice can vary between all scenarios and the set of scenarios charged by a given probability measure. In this way, our framework interpolates between a model with universally acceptable broad assumptions and a model based on a specific probabilistic view of future asset dynamics.
- University of Milan Italy
- University of Oxford United Kingdom
- ETH Zurich Switzerland
- THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD United Kingdom
robust modelling approach, fundamental theorem of asset pricing, FOS: Economics and business, superhedging duality, Derivative securities (option pricing, hedging, etc.), FOS: Mathematics, Optimal stochastic control, Optimality conditions and duality in mathematical programming, Duality theory (optimization), Statistical methods; risk measures, semistatic optimization, arbitrage pricing theory, Probability (math.PR), Optimality conditions for problems involving randomness, Minimax problems in mathematical programming, Robustness in mathematical programming, Mathematical Finance (q-fin.MF), robust modelling approach; fundamental theorem of asset pricing; superhedging duality; semistatic optimization; pointwise stochastic analysis; arbitrage pricing theory; model ambiguity; Knightian uncertainty, Quantitative Finance - Mathematical Finance, Knightian uncertainty, model ambiguity, Martingales with discrete parameter, pointwise stochastic analysis, Mathematics - Probability
robust modelling approach, fundamental theorem of asset pricing, FOS: Economics and business, superhedging duality, Derivative securities (option pricing, hedging, etc.), FOS: Mathematics, Optimal stochastic control, Optimality conditions and duality in mathematical programming, Duality theory (optimization), Statistical methods; risk measures, semistatic optimization, arbitrage pricing theory, Probability (math.PR), Optimality conditions for problems involving randomness, Minimax problems in mathematical programming, Robustness in mathematical programming, Mathematical Finance (q-fin.MF), robust modelling approach; fundamental theorem of asset pricing; superhedging duality; semistatic optimization; pointwise stochastic analysis; arbitrage pricing theory; model ambiguity; Knightian uncertainty, Quantitative Finance - Mathematical Finance, Knightian uncertainty, model ambiguity, Martingales with discrete parameter, pointwise stochastic analysis, Mathematics - Probability
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