Financial Markets in Discrete Time

2018 ◽  
pp. 75-105
Author(s):  
Jia-An Yan
Keyword(s):  
Financial Markets ◽  
Discrete Time

Modeling and asset allocation for financial markets based on a discrete time microstructure model

2003 ◽  
Vol 31 (2) ◽  
pp. 285-293 ◽  
Author(s):  
Hui Peng ◽  
Tohru Ozaki ◽  
Valerie Haggan-Ozaki
Keyword(s):  
Financial Markets ◽  
Discrete Time ◽  
Asset Allocation ◽  
Microstructure Model

FROM DISCRETE-TIME MODELS TO CONTINUOUS-TIME, ASYNCHRONOUS MODELING OF FINANCIAL MARKETS

2007 ◽  
Vol 23 (2) ◽  
pp. 142-161 ◽  
Author(s):  
Katalin Boer ◽  
Uzay Kaymak ◽  
Jaap Spiering
Keyword(s):  
Financial Markets ◽  
Discrete Time ◽  
Continuous Time ◽  
Discrete Time Models

scholarly journals A unified framework for robust modelling of financial markets in discrete time

2021 ◽  
Author(s):  
Jan Obłój ◽  
Johannes Wiesel
Keyword(s):  
Asset Pricing ◽  
Financial Markets ◽  
Discrete Time ◽  
Fundamental Theorem ◽  
Unified Framework ◽  
Martingale Measures ◽  
Robust Modelling

AbstractWe unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in finite discrete time. In particular, we prove a fundamental theorem of asset pricing and a superhedging theorem which encompass the formulations of Bouchard and Nutz [12] and Burzoni et al. [13]. In bringing the two streams of literature together, we examine and compare their many different notions of arbitrage. We also clarify the relation between robust and classical ℙ-specific results. Furthermore, we prove when a superhedging property with respect to the set of martingale measures supported on a set $\Omega $ Ω of paths may be extended to a pathwise superhedging on $\Omega $ Ω without changing the superhedging price.

scholarly journals Asymptotic synthesis of contingent claims with controlled risk in a sequence of discrete‐time markets

2021 ◽  
Vol 16 (1) ◽  
pp. 25-47
Author(s):  
David M. Kreps ◽  
Walter Schachermayer
Keyword(s):  
Financial Markets ◽  
Discrete Time ◽  
Continuous Time ◽  
Contingent Claims ◽  
Contingent Claim ◽  
Complete Markets ◽  
Continuous Time Model ◽  
Time Model ◽  
Black Scholes ◽  
Discrete Time Models

We examine the connection between discrete‐time models of financial markets and the celebrated Black–Scholes–Merton (BSM) continuous‐time model in which “markets are complete.” Suppose that (a) the probability law of a sequence of discrete‐time models converges to the law of the BSM model and (b) the largest possible one‐period step in the discrete‐time models converges to zero. We prove that, under these assumptions, every bounded and continuous contingent claim can be asymptotically synthesized, controlling for the risks taken in a manner that implies, for instance, that an expected‐utility‐maximizing consumer can asymptotically obtain as much utility in the (possibly incomplete) discrete‐time economies as she can at the continuous‐time limit. Hence, in economically significant ways, many discrete‐time models with frequent trading resemble the complete‐markets model of BSM.

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